A proof of Lin's conjecture on inversion sequences avoiding patterns of relation triples

George E. Andrews, Shane Chern

Research output: Contribution to journalArticlepeer-review

Abstract

A sequence e=e1e2⋯en of natural numbers is called an inversion sequence if 0≤ei≤i−1 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 In123) as the set of inversion sequences of length n such that there are no indices 1≤i<j<k≤n 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.

Original languageEnglish (US)
Article number105388
JournalJournal of Combinatorial Theory. Series A
Volume179
DOIs
StatePublished - Apr 2021

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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