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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
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
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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