Publications (18)
Separable elements and splittings in Weyl groups of Type
Ming Liu, Houyi Yu
Separable elements in Weyl groups are generalizations of the well-known class of separable permutations in symmetric groups. Gaetz and Gao showed that for any pair of subse…
Combinatorial equivalence of separable elements in types and
Yong Liao, Yuping Yang, Houyi Yu
We study the combinatorial equivalence of separable elements in types and . A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}…
Sign-twisted generating functions of the odd length for Weyl groups of type
Haihang Gu, Houyi Yu
The odd length in Weyl groups is a new statistic analogous to the classical Coxeter length, and features combinatorial and parity conditions. We establish explicit closed product f…
The coincidence of the Bruhat order and the secondary Bruhat order on
Tao Zhang, Houyi Yu
Given a positive integer and a nonnegative integer with , we denote by the class of all -by- -matrices with constant row and column…
Rigidity for the Hopf algebra of quasi-symmetric functions
Wanwan Jia, Zhengpan Wang, Houyi Yu
We investigate the rigidity for the Hopf algebra of quasisymmetric functions with respect to the monomial, the fundamental and the quasisymmetric Schur basis, respecti…
The weak order on the hyperoctahedral group and the monomial basis for the Hopf algebra of signed permutations
Houyi Yu
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 pro…
Characteristics of Rota-Baxter Algebras
Li Guo, Houyi Yu
The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota-Baxter algebra, called the Rota-Baxter characteristic. We…
On graphs related to co-maximal ideals of a commutative ring
Tongsuo Wu, Meng Ye, Dancheng Lu +1
This paper studies the co-maximal graph $\Om(R)$, the induced subgraph $\G(R)$ of $\Om(R)$ whose vertex set is and a retract $\G_r(R)$ of $\G(R)$, wher…
Renormalization of quasisymmetric functions
Li Guo, Houyi Yu, Bin Zhang
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…
The structure of finite local principal ideal rings
Tongsuo Wu, Houyi Yu, Dancheng Lu
A ring is called a PIR, if each ideal of is a principal ideal. An local ring $(R,\mf{m)}$ is a artinian PIR if and only if its maximal ideal $\mf{m}$ is principal and has f…
On realizing zero-divisor graphs of po-semirings
Houyi Yu, Tongsuo Wu
In this paper, we determine bipartite graphs and complete graphs with horns, which are realizable as zero-divisor graphs of po-semirings. As applications, we classify commutative r…
On the cancellation-free antipode formula for the Malvenuto-Reutenauer Hopf Algebra
Da Xu, Houyi Yu
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)\cdot…
Weak composition quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras
Li Guo, Jean-Yves Thibon, Houyi Yu
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…
Classification of monomial Rota-Baxter operators on k[x]
Houyi Yu
Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial a…
Classification of weak Bruhat interval modules of -Hecke algebras
Yong Liao, Han Yang, Houyi Yu
Weak Bruhat interval modules of the -Hecke algebra in type offer a unified framework for studying modules associated to quasisymmetric functions. This class of modules has r…
Rota--Baxter algebras and left weak composition quasi-symmetric functions
Li Guo, Houyi Yu, Jianqiang Zhao
Motivated by a question of Rota, this paper studies the relationship between Rota--Baxter algebras and symmetric related functions. The starting point is the fact that the space of…
The Hopf algebras of signed permutations, of weak quasi-symmetric functions and of Malvenuto-Reutenauer
Li Guo, Jean-Yves Thibon, Houyi Yu
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-Reutena…
On monomial ideals whose Lyubeznik resolution is minimal
Jin Guo, Tongsuo Wu, Houyi Yu
For a monomial ideal , let be its minimal set of monomial generators. If there is a total order on such that the corresponding Lyubeznik resolution of is a min…