非循环的碎片堆，我
Acyclic heaps of pieces, I
摘要：
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。
英文摘要：
Heaps of pieces were introduced by Viennot and have applications to algebraic combinatorics, theoretical computer science and statistical physics. In this paper, we how certain combinatorial properties of heaps studied by Fan and by Stembridge are closely related to the properties of a certain linear map $\partial_E$ associated to a heap $E$. We examine the relationship between $\partial_E$ and $\partial_F$ when $F$ is a subheap of $E$. This approach allows neat statements and proofs of results on certain associative algebras (generalized Temperley--Lieb algebras) that are otherwise tricky to prove. The key to the proof is to interpret the structure constants of the aforementioned algebras in terms of the maps $\partial$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
