非循环堆件，II

非循环的碎片堆，我

Acyclic heaps of pieces, I

堆件介绍了Viennot和应用代数组合，理论计算机科学和统计物理。在本文中，我们如何某些组合性质的范和Stembridge研究堆是密切相关的性质，一定的线性映射$\partial_E$相关联的堆$E$。当$F$是$E$的一个子堆时，我们研究了$\partial_E$和$\partial_F$之间的关系。这种方法允许整洁的声明和证明某些结合代数（广义Temperley-李伯代数）的结果，否则很难证明。证明的关键是用映射$\partial$来解释上述代数的结构常数。

Kazhdan-Lusztig理论下无圈碎片堆的结构性质

Structural properties of acyclic heaps of pieces with Kazhdan--Lusztig theory

在Viennot的片堆的背景下，我们引入了边界顶点，线性等价和有效边界顶点的概念。证明了在星型可约Coxeter群的全交换元的堆中，每个边界点线性等价于有效边界点。利用这个结果，我们建立了星可约Coxeter群的性质W（在数学QA/0509363意义下），从而纠正了后一篇文章中的一个错误。

Stacked directed animals and multi-directed animals defined without using heaps of pieces

Stacked directed animals and multi-directed animals are two lattice models defined by Bousquet-Mélou and Rechnitzer in 2002. The original definitions of those models involve heaps of pieces, i.e., some geometric representation of partially commutative monoids. The object of this writing is to define stacked directed animals and multi-directed animals in such a way that heaps of pieces are not involved. Our alternative definitions are equivalent to Bousquet-Mélou and Rechnitzer's original ones.

Generalized chromatic polynomials of graphs from Heaps of pieces

Let $G$ be a simple graph and let $\mathcal{L}(G)$ be the free partially commutative Lie algebra associated to $G$. In this paper, using heaps of pieces, we prove an expression for the generalized $\textbf k$-chromatic polynomial of $G$ in terms of dimensions of the grade spaces of $\mathcal{L}(G)$. This will give us a new interpretation for the chromatic polynomials in terms of multilinear heaps and Lyndon length. The classical results of Stanley, and Greene and Zaslavsky regarding the acyclic orientations of $G$ are obtained as corollaries. A heap with a unique minimal piece is said to be a …

用于格路径的片段堆

Heaps of pieces for lattice paths

本文引入格路径的I型与II型片段堆，建立对偶、双射及高维对应，并给出生成函数的行列式与显式公式。

Chromatic Polynomial and Heaps of Pieces

Stanley in his paper [Stanley, Richard P.: Acyclic orientations of graphs In: Discrete Mathematics 5 (1973), Nr. 2, S. 171-178.] provided interpretations of the chromatic polynomial when it is substituted with negative integers. Greene and Zaslavsky interpreted the coefficients of the chromatic polynomial in [Greene, Curtis ; Zaslavsky, Thomas: On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs. In: Transactions of the American Mathematical Society 280 (1983), jan, Nr. 1, S. 97-97.]. We shall develop an invo…