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

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

Abstract 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 …