A refinement of Wilf-equivalence for patterns of length 4

作者：Bloom Jonathan^*

来源：Journal of Combinatorial Theory - Series A, 2014, 124: 166-177.

DOI：10.1016/j.jcta.2014.01.001

• Pattern avoidance
• Bijection
• 2413-avoiding
• 1423-avoiding
• Permutation statistics
• Descents
• Major index

In their paper [6], Dokos at al. conjecture that the major index statistic is equidistributed among 1423-avoiding, 2413-avoiding, and 3214-avoiding permutations. In this paper we confirm this conjecture by constructing two major index preserving bijections, Theta:S-n (1423) -> S-n(2413) and Omega:S-n (3214) -> S-n (2413). In fact, we show that Theta (respectively, Omega) preserves numerous other statistics including the descent set, right-to-left maxima (respectively, left-to-right minima), and a statistic we call steps. Additionally, Theta (respectively, Omega) fixes all permutations avoiding both 1423 and 2413 (respectively, 3214 and 2413).

• 出版日期2014-5