The rank enumeration of certain parabolic non-crossing partitions

被引：0
|
作者：
Krattenthaler, Christian [1 ]
Muehle, Henri [2 ]
机构：
[1] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
[2] Tech Univ Dresden, Inst Algebra, Zellescher Weg 12-14, D-01069 Dresden, Germany
来源：
ALGEBRAIC COMBINATORICS | 2022年 / 5卷 / 03期
关键词：
Non-crossing partition; generating function; Lagrange inversion; zeta polynomial; Dyck path; ballot path; NONCROSSING PARTITIONS; COXETER GROUPS; LATTICE; NUMBERS; CHAINS;
D O I：
10.5802/alco.219
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider m-divisible non-crossing partitions of {1 , 2, ... , mn } with the property that for some t 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.
引用
收藏
页码：437 / 468
页数：33
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