Loading...
Please wait, while we are loading the content...
Similar Documents
New Wilf-equivalence results for dashed patterns
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kasraoui, Anisse |
| Copyright Year | 2012 |
| Abstract | 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 $(X,\leq)$. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1201.4317v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
