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

TL;DR

This paper analyzes the spectral properties and Smith normal form of an incidence matrix associated with disjoint transversals, providing insights into a combinatorial problem related to Rota's basis conjecture.

Contribution

It computes the spectrum and Smith normal form of the incidence matrix linked to disjoint transversals, advancing understanding of Rota's basis conjecture.

Findings

Spectrum of the incidence matrix determined

Smith normal form explicitly computed

Provides algebraic insights into combinatorial structures

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.