Major Index for 01-Fillings of Moon Polyominoes

Details Major Index for 01-Fillings of Moon Polyominoes Major Index for 01-Fillings of Moon Polyominoes

2009-02-20

arxiv.org/abs/0902.3637v1

Mathematics

Combinatorics

28 pages, 14 figures

Scientific paper

We propose a major index statistic on 01-fillings of moon polyominoes which, when specialized to certain shapes, reduces to the major index for permutations and set partitions. We consider the set F(M, s; A) of all 01-fillings of a moon polyomino M with given column sum s whose empty rows are A, and prove that this major index has the same distribution as the number of north-east chains, which are the natural extension of inversions (resp. crossings) for permutations (resp. set partitions). Hence our result generalizes the classical equidistribution results for the permutation statistics inv and maj. Two proofs are presented. The first is an algebraic one using generating functions, and the second is a bijection on 01-fillings of moon polyominoes in the spirit of Foata's second fundamental transformation on words and permutations.

Affiliated with

Also associated with

No associations

Rating

Major Index for 01-Fillings of Moon Polyominoes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Major Index for 01-Fillings of Moon Polyominoes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Major Index for 01-Fillings of Moon Polyominoes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-672056