2007/05/22 by Alexandru Nica, Nica, Alexandru, Ion Oancea +1
Engineering · Mathematics · #06A07 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:06A07
paper · pdf · doi:10.48550/arxiv.0705.3076
Revised version (shortened Introduction, corrected typos), 31 pages, 4 figures, to appear in Discrete Mathematics
openalex publication_date 2007/05/22 · arxiv created 2008/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the set \sncb (p,q) of annular non-crossing permutations of type B, and we introduce a corresponding set \ncb (p,q) of annular non-crossing partitions of type B, where p and q are two positive integers. We prove that the natural bijection between \sncb (p,q) and \ncb (p,q) is a poset isomorphism, where the partial order on \sncb (p,q) is induced from the hyperoctahedral group Bp+q, while \ncb (p,q) is partially ordered by reverse refinement. In the case when q=1, we prove that \ncb (p,1) is a lattice with respect to reverse refinement order. We point out that an analogous development can be pursued in type D, where one gets a canonical isomorphism between \sncd (p,q) and \ncd (p,q). For q=1, the poset \ncd (p,1) coincides with a poset ``NC(D) (p+1)'' constructed in a paper by Athanasiadis and Reiner in 2004, and is a lattice by the results of that paper.