Integer invariants of an incidence matrix related to Rota's basis conjecture

2013/04/07 by Stephanie Bittner, Bittner, Stephanie, Joshua Ducey +7
Mathematics · #05B20 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B20 #msc:05C50

paper · pdf · doi:10.48550/arxiv.1304.2005

v2. Minor changes, added a reference

arxiv created 2013/05/01 · arxiv updated 2013/05/02

Abstract

We compute the spectrum and Smith normal form of the incidence matrix of disjoint transversals, a combinatorial object closely related to the n-dimensional case of Rota's basis conjecture.

Related

• Integer diagonal forms for subset intersection relations
• Smith Normal Form in Combinatorics
• Halfway to Rota's basis conjecture
• Reduction of Rota's basis conjecture to a problem on three bases
• Orthogonal polynomials and Smith normal form