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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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Interval Partitions and Stanley Depth
by
Csaba Biro
University of South Carolina
Coauthors: David M. Howard, Mitchel T. Keller, William T. Trotter, Stephen J. Young

Herzog et al. recently discovered an algorithm that computes the Stanley depth of a monomial ideal of a polynomial ring by considering partitions of certain finite posets into intervals. Motivated by this, they posed the question whether it is possible to partition the nonempty subsets of {1, ..., n} into intervals [Xi, Yi] with |Yi| ≥ n/2. We answer this question affirmatively by giving a construction of such a partition.

Date received: April 9, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-14.