Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655310 | Journal of Combinatorial Theory, Series A | 2014 | 12 Pages |
Abstract
In their paper [6], Dokos et 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, Î:Sn(1423)âSn(2413) and Ω:Sn(3214)âSn(2413). In fact, we show that Î (respectively, Ω) preserves numerous other statistics including the descent set, right-to-left maxima (respectively, left-to-right minima), and a statistic we call steps. Additionally, Î (respectively, Ω) fixes all permutations avoiding both 1423 and 2413 (respectively, 3214 and 2413).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jonathan Bloom,