Clique Decompositions of Strong Short Ladders

Abstract

An explicit recurrence is obtained for the clique polynomial of a short ladder in which the two diagonals are drawn in each cell. From this result, an explicit formula for the number of decompositions of the ladder into triangles and $4$-cliques is obtained. The recurrence is then used to obtain results for the matching polynomial of the ladder. Finally, an association is made with a particular tiling problem.