Moore–Penrose inverse of set inclusion matrices Original Research Article

Given integers s,k and v, let Wsk be the image 0–1 matrix, the rows and the columns of which are indexed by the s-subsets and the k-subsets of a v-set respectively, and where the entry in row S and column U is 1 if Ssubset ofU and 0 otherwise. A formula for the Moore–Penrose inverse of Wsk over the reals is obtained. A necessary and sufficient condition for Wsk to admit a Moore–Penrose inverse over the set of integers modulo a prime p is given, together with a formula for the Moore–Penrose inverse when it exists.