Enumerative techniques for k-inseparable noninclusion and m-noninclusion arrangements

Abstract

Let X = {xt : t = 1, 2, . . . , N} be a finite collection and let K = {xti : i = 1, 2, . . . , k} and M = {xtj : j = 1, 2, . . . ,m} be sub-collections of X. Furthermore, we considered the problem of selecting r(r ≤ n) elements fromX with the k andm non-inclusion elements, such that the k noninclusion elements are always together in each selection. We constructed suitable mathematical formula in the combinatorial sense for enumerative purpose on certain kind of restriction called k-inseparable non-inclusion and m-non-inclusion on the sub-collections of elements of the set X = {xt : t = 1, 2, . . . , N}. Mathematics Subject Classification: 05A10