Enumerative Properties of NC^B(p,q)

Details Enumerative Properties of NC^B(p,q) Enumerative Properties of NC^B(p,q)

2007-08-16

arxiv.org/abs/0708.2212v2

Mathematics

Combinatorics

Revised version -- some corrections and new Section 6 concerning multi-annular partitions of type B. Accepted for publication

Scientific paper

We determine the rank generating function, the zeta polynomial and the Moebius function for the poset NC^B(p,q) of annular non-crossing partitions of type B, where p and q are two positive integers. We give an alternative treatment of some of these results in the case q=1, for which this poset is a lattice. We also consider the general case of multiannular non-crossing partitions of type B, and prove that this reduces to the cases of non-crossing partitions of type B in the annulus and in the disc.

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