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Enumerative Properties of NC(B)(p,q)
I.P. Goulden1, Alexandru Nica2, and Ion Oancea2
1Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
ipgoulden@math.uwaterloo.ca
2Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
anica@uwaterloo.ca, ioancea@alumni.uwaterloo.ca
Annals of Combinatorics 15 (2) pp.277-303 April, 2011
AMS Subject Classification: 06A07, 05A15
Abstract:
We determine the rank generating function, the zeta polynomial and the Möbius 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 noncrossing partitions of type B, and prove that this reduces to the cases of non-crossing partitions of type B in the annulus and the disc.
Keywords: annular non-crossing partitions of type B, rank generating function, zeta polynomial, Möbius function

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