Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Skandera, Mark"'
Publikováno v:
EPTCS 403, 2024, pp. 150-155
We show that coefficients in unicellular LLT polynomials are evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements. We express these in terms of traditional trace bases, induction, and Kazhdan-Lusztig R-polynomials.
Comment: In P
Comment: In P
Externí odkaz:
http://arxiv.org/abs/2406.16414
Autor:
Skandera, Mark, Soskin, Daniel
We characterize ratios of permanents of (generalized) submatrices which are bounded on the set of all totally positive matrices. This provides a permanental analog of results of Fallat, Gekhtman, and Johnson [{\em Adv.\ Appl.\ Math.} {\bf 30} no.\ 3,
Externí odkaz:
http://arxiv.org/abs/2406.00963
Autor:
Skandera, Mark
We state combinatorial formulas for hyperoctahedral group ($\mathfrak B_n$) character evaluations of the form $\chi( {{\widetilde C}_w}^{\negthickspace\negthickspace BC}\negthickspace(1))$, where ${{\widetilde C}_w}^{\negthickspace\negthickspace BC}\
Externí odkaz:
http://arxiv.org/abs/2402.04148
Autor:
Skandera, Mark, Soskin, Daniel
Given a matrix $A$, let $A_{I,J}$ denote the submatrix of $A$ determined by rows $I$ and columns $J$. Fischer's Inequalities state that for each $n \times n$ Hermitian positive semidefinite matrix $A$, and each subset $I$ of $\{1,\dotsc,n\}$ and its
Externí odkaz:
http://arxiv.org/abs/2209.06466
Autor:
Skandera, Mark
Let $P$ be a poset, $inc(P)$ its incomparability graph, and $X_{inc(P)}$ the corresponding chromatic symmetric function, as defined by Stanley in {\em Adv. Math.}, {\bf 111} (1995) pp.~166--194. Certain conditions on $P$ imply that the expansions of
Externí odkaz:
http://arxiv.org/abs/2010.00458
Autor:
Clearwater, Adam, Skandera, Mark
Let $\mathfrak S_{[i,j]}$ be the subgroup of the symmetric group $\mathfrak S_n$ generated by adjacent transpositions $(i,i+1), \dotsc, (j-1,j)$, assuming $1 \leq i < j \leq n$. We give a combinatorial rule for evaluating induced sign characters of t
Externí odkaz:
http://arxiv.org/abs/2007.14512
Autor:
Skandera, Mark
Let $\mathbb Z/d\mathbb Z \wr \mathfrak S_n$ denote the wreath product of the cyclic group $\mathbb Z/d\mathbb Z$ with the symmetric group $\mathfrak S_n$. We define generating functions for monomial (induced one-dimensional) characters of $\mathbb Z
Externí odkaz:
http://arxiv.org/abs/2007.08456
We combinatorially describe entries of the transition matrices which relate monomial bases of the zero-weight space of the quantum matrix bialgebra. This description leads to a combinatorial rule for evaluating induced sign characters of the type $A$
Externí odkaz:
http://arxiv.org/abs/1802.04856
For irreducible characters $\{ \chi_q^\lambda \,|\, \lambda \vdash n \}$, induced sign characters $\{ \epsilon_q^\lambda \,|\, \lambda \vdash n \}$, and induced trivial characters $\{ \eta_q^\lambda \,|\, \lambda \vdash n \}$ of the Hecke algebra $H_
Externí odkaz:
http://arxiv.org/abs/1502.04633
In this series of three articles, we give an exposition of various results and open problems in three areas of algebraic and geometric combinatorics: totally non-negative matrices, representations of the symmetric group, and hyperplane arrangements.
Externí odkaz:
http://arxiv.org/abs/1301.3989