Article ID Journal Published Year Pages File Type
4646750 Discrete Mathematics 2016 10 Pages PDF
Abstract

Björner and Wachs showed that the major index and the inversion number are equidistributed on an order ideal UU of the symmetric group in the weak order if and only if the maximal elements of UU are 132-avoiding permutations. In this paper, we show that the sorting index and the inversion number are equidistributed on an order ideal UU of the symmetric group in the Bruhat order if the maximal elements of UU are 312-avoiding permutations. We also consider the case of type BB. By introducing the notion of BB-increasing subexcedent sequence, we show that the sorting index and inversion number are equidistributed on an order ideal UU of the group of signed permutations in the Bruhat order if the A-code of each maximal element of UU is BB-increasing.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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