Equidistributed statistics on matchings and permutations

Details Equidistributed statistics on matchings and permutations Equidistributed statistics on matchings and permutations

2011-12-09

arxiv.org/abs/1112.2120v1

Mathematics

Combinatorics

26 pages

Scientific paper

We show that the bistatistic of right nestings and right crossings in matchings without left nestings is equidistributed with the number of occurrences of two certain patterns in permutations, and furthermore that this equidistribution holds when refined to positions of these statistics in matchings and permutations. For this distribution we obtain a non-commutative generating function which specializes to Zagier's generating function for the Fishburn numbers after abelianization. As a special case we obtain proofs of two conjectures of Claesson and Linusson. Finally, we conjecture that our results can be generalized to involving left crossings of matchings too.

Affiliated with

Also associated with

No associations

Rating

Equidistributed statistics on matchings and permutations 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 Equidistributed statistics on matchings and permutations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equidistributed statistics on matchings and permutations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-44090