New Wilf-equivalence results for dashed patterns

Details New Wilf-equivalence results for dashed patterns New Wilf-equivalence results for dashed patterns

2012-01-20

arxiv.org/abs/1201.4317v1

Mathematics

Combinatorics

Scientific paper

We give a sufficient condition for the two dashed patterns $\tau^{(1)}-\tau^{(2)}-\cdots-\tau^{(\ell)}$ and $\tau^{(\ell)}-\tau^{(\ell-1)}-\cdots-\tau^{(1)}$ to be (strongly) Wilf-equivalent. This permits to solve in a unified way several problems of Heubach and Mansour on Wilf-equivalences on words and compositions, as well as a conjecture of Baxter and Pudwell on Wilf-equivalences on permutations. We also give a better explanation of the equidistribution of the parameters $\MAK+\bMAJ$ and $\MAK'+\bMAJ$ on ordered set partitions. These results can be viewed as consequences of a simple proposition which states that the set valued statistics "descent set'' and "rise set'' are equidistributed over each equivalence class of the partially commutative monoid generated by a poset $(X,\leq)$.

Affiliated with

Also associated with

No associations

Rating

New Wilf-equivalence results for dashed patterns 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 New Wilf-equivalence results for dashed patterns, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Wilf-equivalence results for dashed patterns will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-321073