Mixed Statistics on 01-Fillings of Moon Polyominoes

The authors establish a stronger symmetry between the numbers of northeast and southeast chains in the context of 01-flings of moon polyominoes. Let M be a moon polyomino with n rows and m columns. Consider all the 01-fillings of M in which every row has at most one 1. They introduce four mixed statistics with respect to a bipartition of rows or columns of M. Similarly, they define the left-mixed and right-mixed statistics ... and ..., where T is a subset of the column index set ... Let ... be any of these four statistics ..., ..., ..., and ...; they show that the joint distribution of the pair ... is symmetric and independent of the subsets S, T. In particular, the pair of statistics ... is equidistributed with (se(M), ne(M)), where se(M) and ne(M) are the numbers of southeast chains and northeast chains of M, respectively.(ProQuest: ... denotes formulae/symbols omitted.)