A Theorem on Higher Bruhat Orders

We show that inclusion order and single-step inclusion coincide for higher Bruhat orders B(n; 2), i.e., B(n; 2) = B (n; 2). Mathematics Subject Classi cations (1991). 06A06, 51G05, 52C99. Key Words. Arrangement of pseudolines, higher Bruhat order. 1 Preliminaries Higher Bruhat orders were introduced by Manin and Schechtman 5] as generalizations of the weak Bruhat order on the symmetric group Sn. Further investigations of the subject are Voevodskij and Kapranov 6], Ziegler 7], Edelman and Reiner 1, 2] and Felsner and Weil 3]. Let us review the de nition. The set n] = f1;::: ;ng is equipped with the natural linear order. The set of s-element subsets of n] is ? n] s . For X 2 ? n] s with s i 1 we let Xbic denote the set X minus the ith-largest element of X (e.g. f3;5;8;9gb2c = f3;8;9g). For a set P 2 ? n] s+1 the set of its s-element subsets fPb1c;Pb2c;::: ;Pbs+1cg is called a s-paket, which we will also denote by P, where this can be done unambigously. Let S be a system of nite sets. The...

• Type: Journal
• Year: 2000
• Where: DCG
• Authors: Stefan Felsner, Helmut Weil
• Keywords: DCG 2000, Inclusion Order, Mathematics Subject Classi, Single-step Inclusion Coincide