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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

A sequence e=e1e2en of natural numbers is called an inversion sequence if 0eii1 for all i{1,2,,n}. Recently, Martinez and Savage initiated an investigation of inversion sequences that avoid patterns of relation triples. Let ρ1, ρ2 and ρ3 be among the binary relations {<,>,,,=,,}. Martinez and Savage defined In(ρ1,ρ2,ρ3) as the set of inversion sequences of length n such that there are no indices 1i<j<kn with eiρ1ej, ejρ2ek and eiρ3ek. In this paper, we will prove a curious identity concerning the ascent statistic over the sets In(>,,) and In(,,>). 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 Ë=Ë1个Ë2Ëñ 的自然数称为反演序列,如果 0Ë一世一世-1个 对全部 一世{1个2ñ}。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ρ1个ρ2ρ3 处于二元关系之中 {<>=-}。马丁内斯和野人的定义一世ñρ1个ρ2ρ3作为长度为n的反转序列的集合,这样就没有索引1个一世<Ĵ<ķñË一世ρ1个ËĴËĴρ2ËķË一世ρ3Ëķ。在本文中,我们将证明关于集合的上升统计的奇异身份一世ñ>一世ñ>。这证实了林志聪最近的猜想。

更新日期:2020-12-20
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