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A proof of Lin's conjecture on inversion sequences avoiding patterns of relation triples
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2020-12-18 , DOI: 10.1016/j.jcta.2020.105388 George E. Andrews , Shane Chern
中文翻译:
关于逆序列避免关系三元模式的Lin猜想的证明
更新日期:2020-12-20
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2020-12-18 , DOI: 10.1016/j.jcta.2020.105388 George E. Andrews , Shane Chern
A sequence of natural numbers is called an inversion sequence if for all . Recently, Martinez and Savage initiated an investigation of inversion sequences that avoid patterns of relation triples. Let , and be among the binary relations . Martinez and Savage defined as the set of inversion sequences of length n such that there are no indices with , and . In this paper, we will prove a curious identity concerning the ascent statistic over the sets and . This confirms a recent conjecture of Zhicong Lin.
中文翻译:
关于逆序列避免关系三元模式的Lin猜想的证明
一个序列 的自然数称为反演序列,如果 对全部 。最近,马丁内斯(Martinez)和萨维奇(Savage)发起了一项反序列的研究,该序列避免了关系三元组的模式。让, 和 处于二元关系之中 。马丁内斯和野人的定义作为长度为n的反转序列的集合,这样就没有索引 与 , 和 。在本文中,我们将证明关于集合的上升统计的奇异身份 和 。这证实了林志聪最近的猜想。