Categorification of Integer Sequences via Brauer Configuration Algebras and the Four Subspace Problem

Abstract

The four subspace problem is a known matrix problem, which is equivalent to determining all the indecomposable representations of a poset consisting of four incomparable points. In this paper, we use solutions of this problem and invariants associated with indecomposable projective modules with some suitable Brauer configuration algebras to categorify the integer sequence encoded in the OEIS as A100705 and some related integer sequences.