CAJ | 학술논문

A=(aij)表示→m×n阶矩阵。可把偏序集PA和A自然联系起来。用X={x1，x2，…xn｜和y={y1，y2，…yn}表示不交的m和n元集，定义xi<yj当且仅当aij≠0。PA的Hasse图就是通常A的二部图，其中ysxs的上面。称PA为二部偏序集。偏序集PA的跳跃[阶梯]数是最小[最大]跳跃[阶梯]的数目。(PA的线性扩张中的一个跳跃是PA中一对不可比较的元素，否则称为阶梯)。文章主要研究了二部偏序集的跳跃数和其Hasse图结构的关系，并给出一个确定PA阶梯数的递归算法。
A=(aij)표시→m×n계구진。가파편서집PA화A자연련계기래。용X={x1，x2，…xn｜화y={y1，y2，…yn}표시불교적m화n원집，정의xi<yj당차부당aij≠0。PA적Hasse도취시통상A적이부도，기중ysxs적상면。칭PA위이부편서집。편서집PA적도약[계제]수시최소[최대]도약[계제]적수목。(PA적선성확장중적일개도약시PA중일대불가비교적원소，부칙칭위계제)。문장주요연구료이부편서집적도약수화기Hasse도결구적관계，병급출일개학정PA계제수적체귀산법。
Let A = (αij)heanm×nmatrix. 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 andn elements, respectively, and define xi < yj if and only if αij ≠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 [rnaximum]number of junps [stairs]in any linear extension of PA . (A jump in a linear extension of PA is a pair of consecutive dements which are incoomparable in PA , otherwise, we call it a stair of PA . ) 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 cliagram of PA .