Balanced simplicial complex associated with 1 × p polyomino

Abstract

Balanced simplicial complexes are important objects in combinatorics and commutative algebra. A d -dimensional simplicial complex is balanced if its vertices can be coloured into d +1 colors, so there is no monochromatic edge. In this article, we establish two results concerning balanced simplicial complexes assigned to tilings of m × n board in a plane and a torus by I p -omino tile