Counting linear extension majority cycles in partially ordered sets on up to 13 elements

Authors:
K. De Loof;B. De Baets;H. De Meyer
Affiliations:
Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 8
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Abstract

It is well known that the linear extension majority relation of a partially ordered set (P,@?"P) can contain cycles when at least 9 elements are present in P. Computer experiments have uncovered all posets with 9 elements containing such cycles and limited frequency estimates for linear extension majority cycles (or LEM cycles) in posets on up to 12 elements are available. In this contribution, we present an efficient approach which allows us to count and store all posets containing LEM cycles on up to 13 elements.