Burstein's permutation conjecture, Hong and Li's inversion sequence conjecture, and restricted Eulerian distributions

09/25/2022

∙

by   Shane Chern, et al.

∙

0

∙

share

Recently, Hong and Li launched a systematic study of length-four pattern avoidance in inversion sequences, and in particular, they conjectured that the number of 0021-avoiding inversion sequences can be enumerated by the OEIS entry A218225. Meanwhile, Burstein suggested that the same sequence might also count three sets of pattern restricted permutations. The objective of this paper is not only a confirmation of Hong and Li's conjecture and Burstein's first conjecture, but also two more delicate generating function identities with the 𝗂𝖽𝖾𝗌 statistic concerned in the restricted permutation case, and the 𝖺𝗌𝖼 statistic concerned in the restricted inversion sequence case, which yield a new equidistribution result.