HAL (Le Centre pour la Communication Scientifique Directe), May 17, 2006
The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in... more The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this article, we study some properties of this polynomial on plane trees. In [5], they show that two different trees could have the same avalanche polynomial. We show here that the problem of finding a tree with a prescribed polynomial is NP-complete. In a second part, we study the average and the variance of the avalanche distribution on trees and give a closed formula.
The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in... more The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this article, we study some properties of this polynomial on plane trees. In [5], they show that two different trees could have the same avalanche polynomial. We show here that the problem of finding a tree with a prescribed polynomial is NP-complete. In a second part, we study the average and the variance of the avalanche distribution on trees and give a closed formula.
We define a solitary game, the Yamanouchi toppling game, on any connected graph of n vertices. Th... more We define a solitary game, the Yamanouchi toppling game, on any connected graph of n vertices. The game arises from the well-known chip-firing game when the usual relation of equivalence defined on the set of all configurations is replaced by a suitable partial order. The set all firing sequences of length m that the player is allowed to perform in the Yamanouchi toppling game is shown to be in bijection with all standard Young tableaux whose shape is a partition of the integer m with at most n−1 parts. The set of all configurations that a player can obtain from a starting configuration is encoded in a suitable formal power series. When the graph is the simple path and each monomial of the series is replaced by a suitable Schur polynomial, we prove that such a series reduces to Hall-Littlewod symmetric polynomials. The same series provides a combinatorial description of orthogonal polynomials when the monomials are replaced by products of moments suitably modified.
On genuinely time bounded computations.- Unified Algebras and action semantics.- Properties of in... more On genuinely time bounded computations.- Unified Algebras and action semantics.- Properties of infinite words : Recent results.- A first order logic for partial functions.- Observational implementations.- On the boundary of a union of Rays.- Dynamic planar point location with optimal query time.- An O(n log n) algorithm for computing a link center in a simple polygon.- Polynomial graph-colorings.- Time-optimal simulations of networks by universal parallel computers.- Classes of picture languages that cannot be distinguished in the chain code concept and deletion of redundant retreats.- Linear numeration systems, ?-developments and finite automata.- A generalization of automatic sequences.- Word problems over traces which are solvable in linear time.- Computing minimum spanning forests on 1- and 2-dimensional processor arrays.- Parallel computation of discrete Voronoi diagrams.- Successive approximation in parallel graph algorithms.- Reversals and alternation.- On the power of parity polynomial time.- Complete problems and strong polynomial reducibilities.- If deterministic and nondeterministic space complexities are equal for log log n then they are also equal for log n.- On the complexity of approximating the independent set problem.- Average number of messages for distributed leader finding in rings of processors.- Time vs bits.- Distributed computing on transitive networks: The torus.- Time is not a healer.- Area efficient methods to increase the reliability of combinatorial circuits.- Fault masking probabilities with single and multiple signature analysis.- Chain properties of rule closures.- It is undecidable whether the Knuth-Bendix completion procedure generates a crossed pair.- Algebraic specifications for domain theory.- The query topology in logic programming.- Testing membership: Beyond permutation groups.- Membership in polynomial ideals over Q is exponential space complete.- Some complexity theoretic aspects of AC rewriting.- Deciding bisimulation equivalences for a class of non-finite-state programs.- Measure of parallelism of distributed computations.- Decidability of weak fairness in petri nets.- New results on the generalized star-height problem.- On the equivalence problem for deterministic multitape automata and transducers.- Deciding equivalence of finite tree automata.- Concatenable segment trees.- Shortest edge-disjoint paths in graphs.- Rounds versus time for the two person pebble game.- AXE: the syntax driven diagram editor for visual languages used in the software engineering environments AxIS.- GraphEd: An interactive graph editor.- SAMPLE a language dependent prototyping environment.- Examining the satisfiability of the formulas of Propositional Dynamic Logic.- Amore: A system for computing automata, MOnoids, and regular expressions.- A proof system for type theory and CCS.- Implementation of a transition semantics for parallel programs with shared variables.
L'accès aux archives de la collection « Séminaire Schützenberger » implique l'accord avec les con... more L'accès aux archives de la collection « Séminaire Schützenberger » implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques
We show that, for any fixed genus g, the ordinary generating function for the genus g partitions ... more We show that, for any fixed genus g, the ordinary generating function for the genus g partitions of an n-element set into k blocks is algebraic. The proof involves showing that each such partition may be reduced in a unique way to a primitive partition and that the number of primitive partitions of a given genus is finite. We illustrate our method by finding the generating function for genus 2 partitions, after identifying all genus 2 primitive partitions, using a computer-assisted search.
Let the consensus number of a given set S\mathcal{S} of shared objects, denoted CN(S)\mathcal{C}\... more Let the consensus number of a given set S\mathcal{S} of shared objects, denoted CN(S)\mathcal{C}\mathcal{N}(\mathcal{S}), be the maximum number n such that there is a wait-free consensus protocol for n distinct processes, which communicate only by accessing objects in S\mathcal{S}.
Journal of Combinatorial Theory, Series A, Sep 1, 1986
A formula for the number alternating Baxter permutations is given. The proof of this formula is g... more A formula for the number alternating Baxter permutations is given. The proof of this formula is given by constructing bijection between permutations, trees, and words. This gives also a combinatorial proof of a formula appearing in the enumerative theory of planar maps.
... Canada) Voronoi Diagrams based on General Metrics in the Plane 281 N. Santoro, JB Sidney, S J... more ... Canada) Voronoi Diagrams based on General Metrics in the Plane 281 N. Santoro, JB Sidney, S J. Sidney, J. Umitia ... Boissonnat (Sophia Antipolis, France) Polygon Placement under Translation and Rotation 322 Trace Languages D. Bruschi, G. Pighizzini, N. Sabadini (Milano ...
R&um&. W. Zielonka a ticemment introduit une famille d'automates finis ayant un fonctioszement pa... more R&um&. W. Zielonka a ticemment introduit une famille d'automates finis ayant un fonctioszement particulier: les automates asynchrones; ceux-ci constituent un modile pour des processus parrrlliles 6changeant des informations par l'intermidiaire de certaines mCmoires communes. Dans ce qui suit, nous introduisons une restriction de la classe de ces automates & celle que nous sppeions 2-asynchrones; cette classe est illustrie par un exemple de probltme de communication faisant intervenir des boites aux lettres. Nous dgmontrons que les automates 2-asynchrones ont la meme puissance que les automates asynchrones g&tCraux. Abstract. W. Zielonka has recently introduced a family of finite automata with a specific behavior, and called them asynchronous automata. 'They can be considered as a good model to describe concurrent processes exchanging data by means of some common storage. Hereafter, we restrict the family of asynchronous automata by defining the subclass of what we will cait 2-asynchronous automata. We illustrate this subclass by a communication problem involving mailboxes, and prove that 2-asynchronous automata are as powerful as asynchonous ones.
The number of spanning trees in a graph is often called it's complexity [1]. A tree is of cou... more The number of spanning trees in a graph is often called it's complexity [1]. A tree is of course of complexity one and it is a classical result of Cayley that the complete graph Kn has complexity nn-2. Between these two numbers lies the complexity of a connected graph. In the case of planar maps it is well-known that a map and its dual have equal complexity (see for instance [2]). in this communication we show that a similar result holds for hypermaps. To prove this result we use a diagram containing six hypermaps which is very related to W.T. Tutte's Trinity [9]. All the needed definitions are recalled. We thus give a few details about hypermaps, their underlying hypergraphs and the maps associated to them. The definition of a spanning hypertree is also given.
Parking functions are central in many aspects of combinatorics. We deÿne in this communication a ... more Parking functions are central in many aspects of combinatorics. We deÿne in this communication a generalization of parking functions which we call (p1; : : : ; p k)-parking functions. We give a characterization of them in terms of parking functions and we show that they can be interpreted as recurrent conÿgurations in the sandpile model for some graphs. We also establish a correspondence with a Lukasiewicz language, which enables to enumerate (p1; : : : ; p k)-parking functions as well as increasing ones. Rà esumà e Les suites de parking se sont rà evà elà eesêtre au centre de di à erents probl emes combinatoires. Nous introduisons ici des k-uplets de suites qui les gà enà eralisent, et dont nous montrons qu'ils peuventêtre interprà età es comme les conÿgurations rà ecurrentes de l'automate du tas de sable sur certains graphes. Nous à etablissons à egalement une correspondance avec un langage de Lukasiewicz, ce qui nous permet d'obtenir des rà esultats d'à enumà eration.
Different formulas counting families of non-isomorphic chord diagrams are given: planar and toroi... more Different formulas counting families of non-isomorphic chord diagrams are given: planar and toroidal ones and those of maximal genus. These formulas are obtained establishing results on the structure of the automorphism group of diagrams of a given genus.
HAL (Le Centre pour la Communication Scientifique Directe), May 17, 2006
The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in... more The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this article, we study some properties of this polynomial on plane trees. In [5], they show that two different trees could have the same avalanche polynomial. We show here that the problem of finding a tree with a prescribed polynomial is NP-complete. In a second part, we study the average and the variance of the avalanche distribution on trees and give a closed formula.
The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in... more The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this article, we study some properties of this polynomial on plane trees. In [5], they show that two different trees could have the same avalanche polynomial. We show here that the problem of finding a tree with a prescribed polynomial is NP-complete. In a second part, we study the average and the variance of the avalanche distribution on trees and give a closed formula.
We define a solitary game, the Yamanouchi toppling game, on any connected graph of n vertices. Th... more We define a solitary game, the Yamanouchi toppling game, on any connected graph of n vertices. The game arises from the well-known chip-firing game when the usual relation of equivalence defined on the set of all configurations is replaced by a suitable partial order. The set all firing sequences of length m that the player is allowed to perform in the Yamanouchi toppling game is shown to be in bijection with all standard Young tableaux whose shape is a partition of the integer m with at most n−1 parts. The set of all configurations that a player can obtain from a starting configuration is encoded in a suitable formal power series. When the graph is the simple path and each monomial of the series is replaced by a suitable Schur polynomial, we prove that such a series reduces to Hall-Littlewod symmetric polynomials. The same series provides a combinatorial description of orthogonal polynomials when the monomials are replaced by products of moments suitably modified.
On genuinely time bounded computations.- Unified Algebras and action semantics.- Properties of in... more On genuinely time bounded computations.- Unified Algebras and action semantics.- Properties of infinite words : Recent results.- A first order logic for partial functions.- Observational implementations.- On the boundary of a union of Rays.- Dynamic planar point location with optimal query time.- An O(n log n) algorithm for computing a link center in a simple polygon.- Polynomial graph-colorings.- Time-optimal simulations of networks by universal parallel computers.- Classes of picture languages that cannot be distinguished in the chain code concept and deletion of redundant retreats.- Linear numeration systems, ?-developments and finite automata.- A generalization of automatic sequences.- Word problems over traces which are solvable in linear time.- Computing minimum spanning forests on 1- and 2-dimensional processor arrays.- Parallel computation of discrete Voronoi diagrams.- Successive approximation in parallel graph algorithms.- Reversals and alternation.- On the power of parity polynomial time.- Complete problems and strong polynomial reducibilities.- If deterministic and nondeterministic space complexities are equal for log log n then they are also equal for log n.- On the complexity of approximating the independent set problem.- Average number of messages for distributed leader finding in rings of processors.- Time vs bits.- Distributed computing on transitive networks: The torus.- Time is not a healer.- Area efficient methods to increase the reliability of combinatorial circuits.- Fault masking probabilities with single and multiple signature analysis.- Chain properties of rule closures.- It is undecidable whether the Knuth-Bendix completion procedure generates a crossed pair.- Algebraic specifications for domain theory.- The query topology in logic programming.- Testing membership: Beyond permutation groups.- Membership in polynomial ideals over Q is exponential space complete.- Some complexity theoretic aspects of AC rewriting.- Deciding bisimulation equivalences for a class of non-finite-state programs.- Measure of parallelism of distributed computations.- Decidability of weak fairness in petri nets.- New results on the generalized star-height problem.- On the equivalence problem for deterministic multitape automata and transducers.- Deciding equivalence of finite tree automata.- Concatenable segment trees.- Shortest edge-disjoint paths in graphs.- Rounds versus time for the two person pebble game.- AXE: the syntax driven diagram editor for visual languages used in the software engineering environments AxIS.- GraphEd: An interactive graph editor.- SAMPLE a language dependent prototyping environment.- Examining the satisfiability of the formulas of Propositional Dynamic Logic.- Amore: A system for computing automata, MOnoids, and regular expressions.- A proof system for type theory and CCS.- Implementation of a transition semantics for parallel programs with shared variables.
L'accès aux archives de la collection « Séminaire Schützenberger » implique l'accord avec les con... more L'accès aux archives de la collection « Séminaire Schützenberger » implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques
We show that, for any fixed genus g, the ordinary generating function for the genus g partitions ... more We show that, for any fixed genus g, the ordinary generating function for the genus g partitions of an n-element set into k blocks is algebraic. The proof involves showing that each such partition may be reduced in a unique way to a primitive partition and that the number of primitive partitions of a given genus is finite. We illustrate our method by finding the generating function for genus 2 partitions, after identifying all genus 2 primitive partitions, using a computer-assisted search.
Let the consensus number of a given set S\mathcal{S} of shared objects, denoted CN(S)\mathcal{C}\... more Let the consensus number of a given set S\mathcal{S} of shared objects, denoted CN(S)\mathcal{C}\mathcal{N}(\mathcal{S}), be the maximum number n such that there is a wait-free consensus protocol for n distinct processes, which communicate only by accessing objects in S\mathcal{S}.
Journal of Combinatorial Theory, Series A, Sep 1, 1986
A formula for the number alternating Baxter permutations is given. The proof of this formula is g... more A formula for the number alternating Baxter permutations is given. The proof of this formula is given by constructing bijection between permutations, trees, and words. This gives also a combinatorial proof of a formula appearing in the enumerative theory of planar maps.
... Canada) Voronoi Diagrams based on General Metrics in the Plane 281 N. Santoro, JB Sidney, S J... more ... Canada) Voronoi Diagrams based on General Metrics in the Plane 281 N. Santoro, JB Sidney, S J. Sidney, J. Umitia ... Boissonnat (Sophia Antipolis, France) Polygon Placement under Translation and Rotation 322 Trace Languages D. Bruschi, G. Pighizzini, N. Sabadini (Milano ...
R&um&. W. Zielonka a ticemment introduit une famille d'automates finis ayant un fonctioszement pa... more R&um&. W. Zielonka a ticemment introduit une famille d'automates finis ayant un fonctioszement particulier: les automates asynchrones; ceux-ci constituent un modile pour des processus parrrlliles 6changeant des informations par l'intermidiaire de certaines mCmoires communes. Dans ce qui suit, nous introduisons une restriction de la classe de ces automates & celle que nous sppeions 2-asynchrones; cette classe est illustrie par un exemple de probltme de communication faisant intervenir des boites aux lettres. Nous dgmontrons que les automates 2-asynchrones ont la meme puissance que les automates asynchrones g&tCraux. Abstract. W. Zielonka has recently introduced a family of finite automata with a specific behavior, and called them asynchronous automata. 'They can be considered as a good model to describe concurrent processes exchanging data by means of some common storage. Hereafter, we restrict the family of asynchronous automata by defining the subclass of what we will cait 2-asynchronous automata. We illustrate this subclass by a communication problem involving mailboxes, and prove that 2-asynchronous automata are as powerful as asynchonous ones.
The number of spanning trees in a graph is often called it's complexity [1]. A tree is of cou... more The number of spanning trees in a graph is often called it's complexity [1]. A tree is of course of complexity one and it is a classical result of Cayley that the complete graph Kn has complexity nn-2. Between these two numbers lies the complexity of a connected graph. In the case of planar maps it is well-known that a map and its dual have equal complexity (see for instance [2]). in this communication we show that a similar result holds for hypermaps. To prove this result we use a diagram containing six hypermaps which is very related to W.T. Tutte's Trinity [9]. All the needed definitions are recalled. We thus give a few details about hypermaps, their underlying hypergraphs and the maps associated to them. The definition of a spanning hypertree is also given.
Parking functions are central in many aspects of combinatorics. We deÿne in this communication a ... more Parking functions are central in many aspects of combinatorics. We deÿne in this communication a generalization of parking functions which we call (p1; : : : ; p k)-parking functions. We give a characterization of them in terms of parking functions and we show that they can be interpreted as recurrent conÿgurations in the sandpile model for some graphs. We also establish a correspondence with a Lukasiewicz language, which enables to enumerate (p1; : : : ; p k)-parking functions as well as increasing ones. Rà esumà e Les suites de parking se sont rà evà elà eesêtre au centre de di à erents probl emes combinatoires. Nous introduisons ici des k-uplets de suites qui les gà enà eralisent, et dont nous montrons qu'ils peuventêtre interprà età es comme les conÿgurations rà ecurrentes de l'automate du tas de sable sur certains graphes. Nous à etablissons à egalement une correspondance avec un langage de Lukasiewicz, ce qui nous permet d'obtenir des rà esultats d'à enumà eration.
Different formulas counting families of non-isomorphic chord diagrams are given: planar and toroi... more Different formulas counting families of non-isomorphic chord diagrams are given: planar and toroidal ones and those of maximal genus. These formulas are obtained establishing results on the structure of the automorphism group of diagrams of a given genus.
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