## Abstract

A sequence e=e_{1}e_{2}⋯e_{n} of natural numbers is called an inversion sequence if 0≤e_{i}≤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 ρ_{1}, ρ_{2} and ρ_{3} be among the binary relations {<,>,≤,≥,=,≠,−}. Martinez and Savage defined I_{n}(ρ_{1},ρ_{2},ρ_{3}) as the set of inversion sequences of length n such that there are no indices 1≤i<j<k≤n with e_{i}ρ_{1}e_{j}, e_{j}ρ_{2}e_{k} and e_{i}ρ_{3}e_{k}. In this paper, we will prove a curious identity concerning the ascent statistic over the sets I_{n}(>,≠,≥) and I_{n}(≥,≠,>). 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