3 lines
11 KiB
Plaintext
3 lines
11 KiB
Plaintext
{"author":[{"fullname":"Levande, Paul","name":"Paul","surname":"Levande","rank":1,"pid":null}],"type":"publication","language":{"code":"eng","label":"English"},"country":[],"maintitle":"Special Cases of the Parking Functions Conjecture and Upper-Triangular Matrices","subtitle":null,"description":["We examine the $q=1$ and $t=0$ special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to the bivariate generating function of $area$ and $dinv$ over the set of parking functions. Haglund recently proved that the Hilbert series for the space of diagonal harmonics is equal to a bivariate generating function over the set of Tesler matrices–upper-triangular matrices with every hook sum equal to one. We give a combinatorial interpretation of the Haglund generating function at $q=1$ and prove the corresponding case of the parking functions conjecture (first proven by Garsia and Haiman). We also discuss a possible proof of the $t = 0$ case consistent with this combinatorial interpretation. We conclude by briefly discussing possible refinements of the parking functions conjecture arising from this research and point of view. $\\textbf{Note added in proof}$: We have since found such a proof of the $t = 0$ case and conjectured more detailed refinements. This research will most likely be presented in full in a forthcoming article.","On examine les cas spéciaux $q=1$ et $t=0$ de la conjecture des fonctions de stationnement. Cette conjecture déclare que la série de Hilbert pour l'espace des harmoniques diagonaux est égale à la fonction génératrice bivariée (paramètres $area$ et $dinv$) sur l'ensemble des fonctions de stationnement. Haglund a prouvé récemment que la série de Hilbert pour l'espace des harmoniques diagonaux est égale à une fonction génératrice bivariée sur l'ensemble des matrices de Tesler triangulaires supérieures dont la somme de chaque équerre vaut un. On donne une interprétation combinatoire de la fonction génératrice de Haglund pour $q=1$ et on prouve le cas correspondant de la conjecture dans le cas des fonctions de stationnement (prouvé d'abord par Garsia et Haiman). On discute aussi d'une preuve possible du cas $t=0$, cohérente avec cette interprétation combinatoire. On conclut en discutant brièvement les raffinements possibles de la conjecture des fonctions de stationnement de ce point de vue. $\\textbf{Note ajoutée sur épreuve}$: j'ai trouvé depuis cet article une preuve du cas $t=0$ et conjecturé des raffinements possibles. Ces résultats seront probablement présentés dans un article ultérieur."],"publicationdate":"2011-01-01","publisher":null,"embargoenddate":null,"source":["ISSN: 1365-8050","Discrete Mathematics & Theoretical Computer Science","Episciences.org","dmtcs:2940 - Discrete Mathematics & Theoretical Computer Science, 2011-01-01, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)"],"format":[],"contributor":["Coordination Episciences iam"],"coverage":[],"bestaccessright":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/"},"container":null,"documentationUrl":null,"codeRepositoryUrl":null,"programmingLanguage":null,"contactperson":null,"contactgroup":null,"tool":null,"size":null,"version":null,"geolocation":null,"id":"50|06cdd3ff4700::93859bd27121c3ee7c6ee4bfb1790cba","originalId":["oai:episciences.org:dmtcs:2940"],"pid":[],"dateofcollection":"2022-04-12T19:57:46.9Z","lastupdatetimestamp":1663599091226,"projects":null,"context":null,"instance":[{"measures":null,"pid":[],"alternateIdentifier":[{"scheme":"doi","value":"10.46298/dmtcs.2940"}],"license":null,"accessright":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/","openAccessRoute":null},"type":"Article","url":["https://dmtcs.episciences.org/2940"],"articleprocessingcharge":null,"publicationdate":"2011-01-01","refereed":"UNKNOWN","hostedby":{"key":"10|openaire____::6824b298c96ba906a3e6a70593affbf5","value":"Episciences"}}],"eoscIF":null,"subject":{},"keywords":["parking function","Hilbert series","diagonal harmonics","[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]","[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]"],"affiliation":null}
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{"author":[{"fullname":"Blondin, Michael","name":"Michael","surname":"Blondin","rank":1,"pid":null},{"fullname":"Raskin, Mikhail","name":"Mikhail","surname":"Raskin","rank":2,"pid":null}],"type":"publication","language":{"code":"und","label":"Undetermined"},"country":[],"maintitle":"The Complexity of Reachability in Affine Vector Addition Systems with States","subtitle":null,"description":["Vector addition systems with states (VASS) are widely used for the formalverification of concurrent systems. Given their tremendous computationalcomplexity, practical approaches have relied on techniques such as reachabilityrelaxations, e.g., allowing for negative intermediate counter values. It isnatural to question their feasibility for VASS enriched with primitives thattypically translate into undecidability. Spurred by this concern, we pinpointthe complexity of integer relaxations with respect to arbitrary classes ofaffine operations. More specifically, we provide a trichotomy on the complexity of integerreachability in VASS extended with affine operations (affine VASS). Namely, weshow that it is NP-complete for VASS with resets, PSPACE-complete for VASS with(pseudo-)transfers and VASS with (pseudo-)copies, and undecidable for any otherclass. We further present a dichotomy for standard reachability in affine VASS:it is decidable for VASS with permutations, and undecidable for any otherclass. This yields a complete and unified complexity landscape of reachabilityin affine VASS. We also consider the reachability problem parameterized by afixed affine VASS, rather than a class, and we show that the complexitylandscape is arbitrary in this setting."],"publicationdate":"2021-07-20","publisher":null,"embargoenddate":null,"source":["ISSN: 1860-5974","Logical Methods in Computer Science","Episciences.org","lmcs:6872 - Logical Methods in Computer Science, 2021-07-20, Volume 17, Issue 3"],"format":[],"contributor":["Michael Blondin"],"coverage":[],"bestaccessright":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/"},"container":null,"documentationUrl":null,"codeRepositoryUrl":null,"programmingLanguage":null,"contactperson":null,"contactgroup":null,"tool":null,"size":null,"version":null,"geolocation":null,"id":"50|06cdd3ff4700::cd7711c65d518859f1d87056e2c45d98","originalId":["oai:episciences.org:lmcs:7687"],"pid":[],"dateofcollection":"2022-04-12T19:57:21.4Z","lastupdatetimestamp":1663599096765,"projects":null,"context":null,"instance":[{"measures":null,"pid":[],"alternateIdentifier":[{"scheme":"doi","value":"10.46298/lmcs-17(3:3)2021"}],"license":null,"accessright":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/","openAccessRoute":null},"type":"Article","url":["https://lmcs.episciences.org/7687"],"articleprocessingcharge":null,"publicationdate":"2021-07-20","refereed":"UNKNOWN","hostedby":{"key":"10|openaire____::6824b298c96ba906a3e6a70593affbf5","value":"Episciences"}}],"eoscIF":null,"subject":{},"keywords":["Computer Science - Logic in Computer Science","Computer Science - Computational Complexity","Computer Science - Formal Languages and Automata Theory"],"affiliation":null}
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{"author":[{"fullname":"Ward, Mark Daniel","name":"Mark Daniel","surname":"Ward","rank":1,"pid":null},{"fullname":"Szpankowski, Wojciech","name":"Wojciech","surname":"Szpankowski","rank":2,"pid":null}],"type":"publication","language":{"code":"eng","label":"English"},"country":[],"maintitle":"Analysis of the multiplicity matching parameter in suffix trees","subtitle":null,"description":["In a suffix tree, the multiplicity matching parameter (MMP) $M_n$ is the number of leaves in the subtree rooted at the branching point of the $(n+1)$st insertion. Equivalently, the MMP is the number of pointers into the database in the Lempel-Ziv '77 data compression algorithm. We prove that the MMP asymptotically follows the logarithmic series distribution plus some fluctuations. In the proof we compare the distribution of the MMP in suffix trees to its distribution in tries built over independent strings. Our results are derived by both probabilistic and analytic techniques of the analysis of algorithms. In particular, we utilize combinatorics on words, bivariate generating functions, pattern matching, recurrence relations, analytical poissonization and depoissonization, the Mellin transform, and complex analysis."],"publicationdate":"2005-01-01","publisher":null,"embargoenddate":null,"source":["ISSN: 1365-8050","Discrete Mathematics & Theoretical Computer Science","Episciences.org","dmtcs:3387 - Discrete Mathematics & Theoretical Computer Science, 2005-01-01, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms"],"format":[],"contributor":["Coordination Episciences iam"],"coverage":[],"bestaccessright":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/"},"container":null,"documentationUrl":null,"codeRepositoryUrl":null,"programmingLanguage":null,"contactperson":null,"contactgroup":null,"tool":null,"size":null,"version":null,"geolocation":null,"id":"50|06cdd3ff4700::ff21e3c55d527fa7db171137c5fd1f1f","originalId":["oai:episciences.org:dmtcs:3387"],"pid":[],"dateofcollection":"2022-04-12T19:57:43.247Z","lastupdatetimestamp":1663599101233,"projects":null,"context":null,"instance":[{"measures":null,"pid":[],"alternateIdentifier":[{"scheme":"doi","value":"10.46298/dmtcs.3387"}],"license":null,"accessright":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/","openAccessRoute":null},"type":"Article","url":["https://dmtcs.episciences.org/3387"],"articleprocessingcharge":null,"publicationdate":"2005-01-01","refereed":"UNKNOWN","hostedby":{"key":"10|openaire____::6824b298c96ba906a3e6a70593affbf5","value":"Episciences"}}],"eoscIF":null,"subject":{},"keywords":["data compression","complex asymptotics","suffix trees","combinatorics on words","pattern matching","autocorrelation polynomial","[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]","[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]","[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]","[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]"],"affiliation":null} |