On distribution of the depth index on perfect matchings

Yonah Cherniavsky, Yuval Khachatryan-Raziel

Published 2022-02-10Version 1

We study the restriction of depth index statistic on the set of perfect matchings. In particular, we provide additional combinatorial description of the statistic for perfect matchings and calculate the generating polynomial. The main result of the present short paper is that the depth index on perfect matchings is equidistributed with the rank function of the Bruhat order.