Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Yu, Houyi"'
Weak Bruhat interval modules of the $0$-Hecke algebra in type $A$ provide a uniform approach to studying modules associated with noteworthy families of quasisymmetric functions. Recently this kind of modules were generalized from type $A$ to all Coxe
Externí odkaz:
http://arxiv.org/abs/2410.07990
Autor:
Gu, Haihang, Yu, Houyi
The odd length in Weyl groups is a new statistic analogous to the classical Coxeter length, and features combinatorial and parity conditions. We establish an explicit closed product formula for the sign-twisted generating functions of the odd length
Externí odkaz:
http://arxiv.org/abs/2303.07658
Publikováno v:
European J. Combin.113 (2023) 103745
For the Malvenuto-Reutenauer Hopf algebra of permutations, we provide a cancellation-free antipode formula for any permutation of the form $ab1\cdots(b-1)(b+1)\cdots(a-1)(a+1)\cdots n$, which starts with the decreasing sequence $ab$ and ends with the
Externí odkaz:
http://arxiv.org/abs/2208.06841
Autor:
Zhang, Tao, Yu, Houyi
Given a positive integer $n$ and a nonnegative integer $k$ with $k\leq n$, we denote by $\mathcal{A}(n,k)$ the class of all $n$-by-$n$ $(0,1)$-matrices with constant row and column sums $k$. In this paper, we show that the Bruhat order and the second
Externí odkaz:
http://arxiv.org/abs/2208.04572
Autor:
Yu, Houyi
We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted products of hyperoctahedral groups. It is shown that each shifted product
Externí odkaz:
http://arxiv.org/abs/2205.01266
As a natural basis of the Hopf algebra of quasisymmetric functions, monomial quasisymmetric functions are formal power series defined from compositions. The same definition applies to left weak compositions, while leads to divergence for other weak c
Externí odkaz:
http://arxiv.org/abs/2012.11872
Publikováno v:
Advances in Math, vol 374, (2020) 107341
This paper builds on two covering Hopf algebras of the Hopf algebra QSym of quasi-symmetric functions, with linear bases parameterized by compositions. One is the Malvenuto-Reutenauer Hopf algebra SSym of permutations, mapped onto QSym by taking desc
Externí odkaz:
http://arxiv.org/abs/1912.12721
We investigate the rigidity for the Hopf algebra ${\rm QSym}$ of quasisymmetric functions with respect to the monomial, the fundamental and the quasisymmetric Schur basis, respectively. By establishing some combinatorial properties of the posets of c
Externí odkaz:
http://arxiv.org/abs/1712.06499
Publikováno v:
Adv Math. 344 (2019), 1-34
We introduce the Hopf algebra of quasi-symmetric functions with semigroup exponents generalizing the Hopf algebra QSym of quasi-symmetric functions. As a special case we obtain the Hopf algebra WCQSym of weak composition quasi-symmetric functions, wh
Externí odkaz:
http://arxiv.org/abs/1702.08011