论文标题
编码标记为$ p $ -riordan图形图和避开图案的排列
Encoding labelled $p$-Riordan graphs by words and pattern-avoiding permutations
论文作者
论文摘要
$ p $ -Riordan图的概念概括了Riordan图的概念，这又概括了Pascal图和Toeplitz图的概念。在本文中，我们介绍了$ p $ -riordan Word的概念，并通过$ p $ -riordan单词展示如何编码$ p $ -riordan图形。对于Riordan图的特殊重要情况（情况$ p = 2 $）和定向的Riordan图（案例$ p = 3 $），我们分别提供了替代的编码，分别是避免模式的排列和某些平衡的单词。作为我们研究的双重产品，我们提供了在立方体中封闭行走的已知枚举结果的替代证明。
The notion of a $p$-Riordan graph generalizes that of a Riordan graph, which, in turn, generalizes the notions of a Pascal graph and a Toeplitz graph. In this paper we introduce the notion of a $p$-Riordan word, and show how to encode $p$-Riordan graphs by $p$-Riordan words. For special important cases of Riordan graphs (the case $p=2$) and oriented Riordan graphs (the case $p=3$) we provide alternative encodings in terms of pattern-avoiding permutations and certain balanced words, respectively. As a bi-product of our studies, we provide an alternative proof of a known enumerative result on closed walks in the cube.
