• U-COVERING SETS AND U-COVERING POLYNOMIALS OF CHAINS

Abstract

Let P be a finite poset. For a subset A of P, the upper cover set of A is defined as U(A) = {xÎP|x covers an aÎA}. The upper closed neighbours of A is defined as U[A]=U(A)  A and A is called an U – covering set of  P  if  U[A] = P.  The U – covering number (P) is the minimum cardinality of a U-covering set. Let   be the family of all U-covering sets of a chain P_n with cardinality i.  Similarly we can define L – covering and N-covering sets of P_n with cordinality i.  (P_n,i) = ||, (P_n, i) = ||, (P_n, i) = ||.  In this paper, we construct , and obtain a recursive formula for U(P_n,i).  Using this recursive  formula   we  construct  the   polynomial  U(P_n,x) = (P_n,i)xⁱ   called  U-covering polynomial of P_n .