Some remarks on normalized matching

Douglas B West, Lawrence H Harper, David E Daykin
1983 Journal of combinatorial theory. Series A  
A new class of LYM orders is obtained, and several results about general LYM orders are proved. (1) Let A, CA, c ... CA,. be a chain of subsets of [n]= (1,..., n}. Let (a,) and (bj) be two nondecreasing sequences with ai < b, for 1 <i< r. Then (XC [n]: ai < lXnA,l <b,}, ordered by inclusion, is a poset having the LYM property. (2) The smallest regular covering of an LYM order has M(P) chains, where M(P) is the least common multiple of the rank sizes. (3) Every LYM order has a smallest regular
more » ... vering with at most lPi -h(P) classes of distinct chains, where h(P) is the height of P. To obtain (3), we discuss "minimal sets" of covering relations between two adjacent levels of an LYM-order.
doi:10.1016/0097-3165(83)90015-8 fatcat:dkvc62tkc5dnxblxeptopecdl4