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 In(ρ1,ρ2,ρ3) 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 language | English (US) |
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Article number | 105388 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 179 |
DOIs | |
State | Published - Apr 2021 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics