Minkowski decompositions for generalized associahedra of acyclic type

无环偏序多面体及其商

Acyclic Poset Multiplihedra and their Quotients

研究利用图乘法多面体为无环关联多面体定义并实现新的乘法多面体，还对其商进行了研究，最终得出偏序集序多面体的区间多面体，为结合运算组合学提供了新的多面体相关内容。

Minkowski Decomposition of Associahedra and Related Combinatorics

Realisations of associahedra with linearly non-isomorphic normal fans can be obtained by alteration of the right-hand sides of the facet-defining inequalities from a classical permutahedron. These polytopes can be expressed as Minkowski sums and differences of dilated faces of a standard simplex as described by Ardila, Benedetti & Doker (2010). The coefficients $y_I$ of such a Minkowski decomposition can be computed by Möbius inversion if tight right-hand sides $z_I$ are known not just for the facet-defining inequalities of the associahedron but also for all inequalities of the permutahedron t…

球面子词复形的砖多胞形与广义associahedra

Brick polytopes of spherical subword complexes and generalized associahedra

将砖多胞形推广至有限Coxeter群的球面子词复形，为簇复形提供多胞形实现，并给出广义associahedra的顶点描述、Minkowski分解及交换矩阵组合描述。

面嵌套复形与无环嵌套多面体

Facial nested complexes and acyclonestohedra

本文研究有向拟阵面格上嵌套复形的多面体实现，通过将面嵌套复形嵌入布尔嵌套复形并构造无环嵌套多面体，统一推广了偏序集关联多面体等多类嵌套多面体族。

Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

Stringy canonical forms are a class of integrals that provide $α'$-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebra, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type $A_n$ and $B…

Multivariate polynomials for generalized permutohedra

Using the notion of Mahonian statistic on acyclic posets, we introduce a $q$-analogue of the $h$-polynomial of a simple generalized permutohedron. We focus primarily on the case of nestohedra and on explicit computations for many interesting examples, such as $S_n$-invariant nestohedra, graph associahedra, and Stanley--Pitman polytopes. For the usual (Stasheff) associahedron, our generalization yields an alternative $q$-analogue to the well-studied Narayana numbers.