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Burstein’s permutation conjecture, Hong and Li’s inversion sequence conjecture and restricted Eulerian distributions
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 4 / November 2023
- Published online by Cambridge University Press:
- 23 October 2023, pp. 1179-1201
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- Article
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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
$\mathsf{ides}$ statistic concerned in the restricted permutation case and the 
$\mathsf{asc}$ statistic concerned in the restricted inversion sequence case, which yield a new equidistribution result.
