Combinatorics of the symmetries of ascents in restricted inversion
sequences
Combinatorics of the symmetries of ascents in restricted inversion
sequences
The systematic study of inversion sequences avoiding triples of relations was initiated by Martinez and Savage. For a triple $(\rho_1,\rho_2,\rho_3)\in\{<,>,\leq,\geq,=,\neq,-\}^3$, they introduced $\I_n(\rho_1,\rho_2,\rho_3)$ as the set of inversion sequences $e=e_1e_2\cdots e_n$ of length $n$ such that there are no indices $1\leq i<j<k\leq n$ with $e_i \rho_1 e_j$, $e_j \rho_2 e_k$ …