Abstract:Let A=(aij) be an m×n matrix. There is a natural way to associate a poset PA with A. Let X={x1,x2,…,xm} and Y={y1,y2,…,yn} be disjoint sets of m and n elements, respectively, and define xi yj if and o...Let A=(aij) be an m×n matrix. There is a natural way to associate a poset PA with A. Let X={x1,x2,…,xm} and Y={y1,y2,…,yn} be disjoint sets of m and n elements, respectively, and define xi yj if and only if aij ≠0. The Hasse diagram of poset PA is the usual bipartite graph of A with vertex set X U Y drawn with the y's above the x's , and PA is called a bipartite poset. The jump [stair]number of a poset is the minimum [maximum] number of jumps [stairs]in any linear extension of PA. (A jump in a linear extension of PA is a pair of consecutive elements which are incomparable in PA, otherwise, we call it a stair ofPA.) In this paper, we investigate the jump number of bipartite poset and its relation to the Hasse diagram structure. We give a recursive algorithm to determine the stair number of PA which is motivated by consideration of the Hasse diagram of PA.Read More
Publication Year: 2001
Publication Date: 2001-01-01
Language: en
Type: article
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