Simplicial Complexes of Triangular Ferrers Boards

2010/08/26 by Eric Clark, Clark, Eric, Matthew Zeckner +1
Mathematics · #05E45 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E45

paper · pdf · doi:10.48550/arxiv.1008.4525

14 pages, 5 figures

arxiv created 2012/09/26 · arxiv updated 2012/09/27

Abstract

We study the simplicial complex that arises from non-attacking rook placements on a subclass of Ferrers boards that have a_i rows of length i where a_i>0 and i≤ n for some positive integer n. In particular, we will investigate enumerative properties of their facets, their homotopy type, and homology.

Related

• Rook poset equivalence of Ferrers boards
• The inverse rook problem on Ferrers boards
• The Diagonals of a Ferrers Diagram
• A Graph Theory of Rook Placements
• Two Vignettes On Full Rook Placements