Zobrazeno 1 - 10
of 368
pro vyhledávání: '"05E05, 05E10"'
We give a counting formula in terms of modified Hall-Littlewood polynomials and the chromatic quasisymmetric function for the number of points on an arbitrary Hessenberg variety over a finite field. As a consequence, we express the Poincar\'e polynom
Externí odkaz:
http://arxiv.org/abs/2411.05096
Autor:
Graf, John, Jing, Naihuan
Schur functions have been shown to satisfy certain stability properties and recurrence relations. In this paper, we prove analogs of these properties with Schur's $Q$-functions using vertex operator methods.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2409.01479
The dual immaculate and Young quasisymmetric Schur bases of quasisymmetric functions possess analogues in the peak algebra: respectively, the quasisymmetric Schur $Q$-functions and the peak Young quasisymmetric Schur functions. We show elements of th
Externí odkaz:
http://arxiv.org/abs/2406.12751
In this paper, we explore the relationship between quasisymmetric Schur $Q$-functions and peak Young quasisymmetric Schur functions. We introduce a bijection on $\mathsf{SPIT}(\alpha)$ such that $\{\mathrm{w}_{\rm c}(T) \mid T \in \mathsf{SPIT}(\alph
Externí odkaz:
http://arxiv.org/abs/2405.05867
Autor:
Martinez, Alvaro L., Wildon, Mark
Let $\mathbb{F}$ be a field and let $E$ be the natural representation of $\mathrm{SL}_2(\mathbb{F})$. Given a vector space $V$, let $\Delta^{(2,1^{N-1})}V$ be the kernel of the multiplication map $\bigwedge^N V \otimes V \rightarrow \bigwedge^{N+1}V$
Externí odkaz:
http://arxiv.org/abs/2405.04631
A natural unit interval order is a naturally labelled partially ordered set that avoids patterns ${\bf 3} + {\bf 1}$ and $\bf 2 + 2$. To each natural unit interval order one can associate a symmetric function. The Stanley-Stembridge conjecture states
Externí odkaz:
http://arxiv.org/abs/2404.07280
Autor:
Defant, Colin, Searles, Dominic
We extend the notion of ascent-compatibility from symmetric groups to all Coxeter groups, thereby providing a type-independent framework for constructing families of modules of $0$-Hecke algebras. We apply this framework in type $B$ to give represent
Externí odkaz:
http://arxiv.org/abs/2404.04961
It is an important problem in algebraic combinatorics to deduce the Schur function expansion of a symmetric function whose expansion in terms of the fundamental quasisymmetric function is known. For example, formulas are known for the fundamental exp
Externí odkaz:
http://arxiv.org/abs/2404.04512
In a sequence of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc (CMPP) and then M. Primc put forth three remarkable sets of conjectures, stating that the generating functions of coloured integer partition in which the parts satisfy restric
Externí odkaz:
http://arxiv.org/abs/2404.03851
We study a multispecies $t$-PushTASEP system on a finite ring of $n$ sites with site-dependent rates $x_1,\dots,x_n$. Let $\lambda=(\lambda_1,\dots,\lambda_n)$ be a partition whose parts represent the species of the $n$ particles on the ring. We show
Externí odkaz:
http://arxiv.org/abs/2403.10485