Permutation Polytopes

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Article #135

#135

From: Michael Cohen
Date: Sat, 03 Oct 1992 01:26

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Treat the orderings on n letters as permutations.
For each ordering a, define a point in n X n-1/2
space as follows.

U_a(i,j) = 1 if i a j
U_a(i,j) = -1 otherwise.

Consider the convex polytope U which is a convex combination of these
extreme points.  Question:  What is the polar polyhedron.  i.e. the
extreme points of the the of elements <l, u> <= 1. for all u in U.
            -mike



-- 
Boston University (617-353-7857) Email: mike@park.bu.edu
Smail: Michael Cohen                     111 Cummington Street, RM 242
       Center for Adaptive Systems        Boston, Mass 02215
       Boston University

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Path: arc1-ca.pugleaf.net!sparky!uunet!olivea!spool.mu.edu!uwm.edu!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet
From: mike@park.bu.edu (Michael Cohen)
Newsgroups: sci.math.research
Subject: Permutation Polytopes
Summary: Polytopes, extreme points
Keywords: Extreme points
Message-ID: <97468@bu.edu>
Date: 3 Oct 92 01:26:16 GMT
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