| Autor: |
Jessica Striker, Nathan Williams |
| Jazyk: |
angličtina |
| Rok vydání: |
2012 |
| Předmět: |
|
| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AR,..., Iss Proceedings (2012) |
| Druh dokumentu: |
article |
| ISSN: |
1365-8050 |
| DOI: |
10.46298/dmtcs.3038 |
| Popis: |
We present an equivariant bijection between two actions—promotion and rowmotion—on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and certain cases of recent work of D. Armstrong, C. Stump, and H. Thomas on noncrossing and nonnesting partitions. We apply this bijection to several classes of posets, obtaining equivariant bijections to various known objects under rotation. We extend the same idea to give an equivariant bijection between alternating sign matrices under rowmotion and under B. Wieland's gyration. Lastly, we define two actions with related orders on alternating sign matrices and totally symmetric self-complementary plane partitions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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