A new approach to Macaulay posets

Authors:
Sergei L. Bezrukov;Victor P. Piotrowski;Thomas J. Pfaff
Affiliations:
Department of Mathematics and Computer Science, University of Wisconsin--Superior, Superior, WI;Department of Mathematics and Computer Science, University of Wisconsin--Superior, Superior, WI;Mathematics and Computer Science Department, Ithaca College, Ithaca, NY
Venue:
Journal of Combinatorial Theory Series A
Year:
2004

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Abstract

We develop a new approach for establishing the Macaulayness of posets representable as cartesian powers of other posets. This approach is based on a problem of constructing an ideal of maximum rank in a poset. Using the relations between the maximum rank ideal problem and the edge-isoperimetric problem on graphs we demonstrate an application of our approach to specification of all posets with a special Macaulay order. We also present a new general construction for additive Macaulay posets and introduce several new families of Macaulay posets.