The rank enumeration of certain parabolic non-crossing partitions
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
We consider m-divisible non-crossing partitions of {1, 2, . . . ,mn} with the property that for some t 6 n no block contains more than one of the integers 1, 2, . . . , t. We give a closed formula for the number of multi-chains of such non-crossing partitions with prescribed number of blocks. Building on this result, we compute Chapoton's M-triangle in this setting and conjecture a combinatorial interpretation for the H-triangle. This conjecture is proved for m = 1.
Details
Originalsprache | Englisch |
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Seiten (von - bis) | 437-468 |
Seitenumfang | 32 |
Fachzeitschrift | Algebraic Combinatorics |
Jahrgang | 5 |
Ausgabenummer | 3 |
Publikationsstatus | Veröffentlicht - 2022 |
Peer-Review-Status | Ja |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- ballot path, Dyck path, generating function, Lagrange inversion, Non-crossing partition, zeta polynomial