The lexicographic sum of Cohen-Macaulay and shellable ordered sets |
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| Authors: | Jerrold R Griggs Andrew R Kustin Jeffrey A Ross Jürgen Stahl |
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| Institution: | (1) Department of Mathematics and Statistics, University of South Carolina, 29208 Columbia, SC, USA;(2) Present address: Communications Research, 3D-638 Holmdel, NJ 07733, USA;(3) Present address: F64 AG1, Technische Hochschule Darmstadt, Schlossgartenstr. 7, 6100 Darmstadt, Federal Republic of Germany |
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| Abstract: | We study the problem of determining when the lexicographic sum ∑ q∈Q P q of a family of posets {P q/qεQ} over a posetQ is Cohen-Macaulay or shellable. Our main result, a characterization of when the lexicographic sum is Cohen-Macaulay, is proven using combinatorial methods introduced by Garsia. A similar characterization for when the lexicographic sum is CL (chainwise-lexicographically)-shellable, is derived using the recursive atom ordering method due to Björner and Wachs. |
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