Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Ira M. Gessel"'
Autor:
Ira M. Gessel, Yan Zhuang
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
Given a permutation statistic $\operatorname {\mathrm {st}}$ , define its inverse statistic $\operatorname {\mathrm {ist}}$ by . We give a general approach, based on the theory of symmetric functions, for finding the joint distribution of $\oper
Externí odkaz:
https://doaj.org/article/276b89e3d7c94292bcd9bf7d7260fa97
Autor:
Ira M. Gessel, Jiang Zeng
Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of ($q=1$) classical orthogonal polynomials, and study those cases in which the exponential generati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1503bc7839e80b932d4139b95dedd402
Autor:
Ira M. Gessel, Yan Zhuang
Publikováno v:
Advances in Mathematics. 332:85-141
Since the early work of Richard Stanley, it has been observed that several permutation statistics have a remarkable property with respect to shuffles of permutations. We formalize this notion of a shuffle-compatible permutation statistic and introduc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45f9330904ff19fca95613fe9aead504
https://doi.org/10.1016/j.aim.2018.05.003
https://doi.org/10.1016/j.aim.2018.05.003
A descent of a labeled digraph is a directed edge (s, t) with s > t. We count strong tournaments, strong digraphs, and acyclic digraphs by descents and edges. To count strong tournaments we use Eulerian generating functions and to count strong and ac
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da4e6410ddb101c99bf769d2892936de
Autor:
Ira M. Gessel, Yan Zhuang
Publikováno v:
Advances in Mathematics. 375:107370
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic substitutions on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c2100cafcc4df388261c35b08922d5c5
https://doi.org/10.1016/j.aim.2020.107370
https://doi.org/10.1016/j.aim.2020.107370
The ring of cyclic quasi-symmetric functions and its non-Escher subring are introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; for the non-Escher subring they arise as toric $P$-partition enumerators,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c65aa9fdf2bbe50dd93a4b46d753074
http://arxiv.org/abs/1811.05440
http://arxiv.org/abs/1811.05440
Autor:
Ira M. Gessel
Egge, Loehr, and Warrington proved a formula for the Schur function expansion of a symmetric function in terms of its expansion in fundamental quasi-symmetric functions. Their formula involves the coefficients of a modified inverse Kostka matrix. Rec
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4966ac5de8b66ae0b5bcd0f6f37fd26
In 1995, the first author introduced a multivariate generating function {$G$} that tracks the distribution of ascents and descents in labeled binary trees. In addition to proving that $G$ is symmetric, he conjectured that $G$ is Schur positive. We pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e922414bf15811f0272a2f73a57e8a01
Autor:
Ira M. Gessel
Publikováno v:
The Ramanujan Journal. 36:165-170
We give a simple proof of George Andrews’s balanced 5F4 evaluation using two fundamental principles: the nth difference of a polynomial of degree less than n is zero, and a polynomial of degree n that vanishes at n+1 points is identically zero.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::79bca82de5d86e0c3488a5b1941778f8
https://doi.org/10.1007/s11139-013-9517-8
https://doi.org/10.1007/s11139-013-9517-8
Autor:
Ira M. Gessel
Publikováno v:
The Mathematical Legacy of Richard P. Stanley
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1cf6a4df4a7fe3cb64d82f93397fd329
https://doi.org/10.1090//mbk/100/10
https://doi.org/10.1090//mbk/100/10