On 021-Avoiding Ascent Sequences [article]

William Y. C. Chen, Alvin Y. L. Dai, Theodore Dokos, Tim Dwyer, Bruce E. Sagan
2012 arXiv   pre-print
Ascent sequences were introduced by Bousquet-Mélou, Claesson, Dukes and Kitaev in their study of (2+2)-free posets. An ascent sequence of length n is a nonnegative integer sequence x=x_1x_2... x_n such that x_1=0 and x_i≤(x_1x_2...x_i-1)+1 for all 1<i≤ n, where (x_1x_2...x_i-1) is the number of ascents in the sequence x_1x_2... x_i-1. We let _n stand for the set of such sequences and use _n(p) for the subset of sequences avoiding a pattern p. Similarly, we let S_n(τ) be the set of τ-avoiding
more » ... mutations in the symmetric group S_n. Duncan and Steingrímsson have shown that the ascent statistic has the same distribution over _n(021) as over S_n(132). Furthermore, they conjectured that the pair (, ) is equidistributed over _n(021) and S_n(132) where is the right-to-left minima statistic. We prove this conjecture by constructing a bistatistic-preserving bijection.
arXiv:1206.2849v2 fatcat:6gku7f4isvcrflyqk3a5ogzaea