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pro vyhledávání: '"Vassilieva, Ekaterina A."'
Publikováno v:
S\'eminaire Lotharingien de Combinatoire 91B (2024) (Proceedings of the 36th FPSAC) Article #86, 12 pp
In our previous works we introduced a $q$-deformation of the generating functions for enriched $P$-partitions. We call the evaluation of this generating functions on labelled chains, the $q$-fundamental quasisymmetric functions. These functions inter
Externí odkaz:
http://arxiv.org/abs/2406.01166
We construct a new family $\left( \eta_{\alpha}^{\left( q\right) }\right) _{\alpha\in\operatorname*{Comp}}$ of quasisymmetric functions for each element $q$ of the base ring. We call them the "enriched $q$-monomial quasisymmetric functions". When $r:
Externí odkaz:
http://arxiv.org/abs/2309.01118
Publikováno v:
S\'eminaire Lotharingien de Combinatoire 89B (2023), Proceedings of the 35th Conference on Formal Power Series 2023, Article #46
Building up on our previous works regarding $q$-deformed $P$-partitions, we introduce a new family of subalgebras for the ring of quasisymmetric functions. Each of these subalgebras admits as a basis a $q$-analogue to Gessel's fundamental quasisymmet
Externí odkaz:
http://arxiv.org/abs/2301.00309
Publikováno v:
corrected version of: S\'eminaire Lotharingien de Combinatoire, 86B.78 (2022), 12 pp
We introduce a $q$-deformation that generalises in a single framework previous works on classical and enriched $P$-partitions. In particular, we build a new family of power series with a parameter $q$ that interpolates between Gessel's fundamental ($
Externí odkaz:
http://arxiv.org/abs/2202.06153
Publikováno v:
S\'eminaire Lotharingien de Combinatoire, 85B.58 (2021), 12 pp
Gessel's fundamental and Stembridge's peak functions are the generating functions for (enriched) $P$-partitions on labelled chains. They are also the bases of two significant subalgebras of formal power series, respectively the ring of quasisymmetric
Externí odkaz:
http://arxiv.org/abs/2202.04720
Over the past years, major attention has been drawn to the question of identifying Schur-positive sets, i.e. sets of permutations whose associated quasisymmetric function is symmetric and can be written as a non-negative sum of Schur symmetric functi
Externí odkaz:
http://arxiv.org/abs/2012.01885
Akademický článek
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Autor:
Vassilieva, Ekaterina A.
The connection between the generating functions of various sets of tableaux and the appropriate families of quasisymmetric functions is a significant tool to give a direct analytical proof of some advanced bijective results and provide new combinator
Externí odkaz:
http://arxiv.org/abs/1911.10430
Akademický článek
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Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the $b$-conjecture) are two major open questions relating Jack symmetric functions, the representation theory of the
Externí odkaz:
http://arxiv.org/abs/1712.08246