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Skeletons of monomial ideals
Author(s) -
Herzog Jürgen,
Jahan Ali Soleyman,
Zheng Xinxian
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810039
Subject(s) - monomial , monomial ideal , conjecture , mathematics , ideal (ethics) , analogy , combinatorics , resolution (logic) , pure mathematics , polynomial , polynomial ring , computer science , mathematical analysis , law , artificial intelligence , linguistics , philosophy , political science
In analogy to the skeletons of a simplicial complex and their Stanley–Reisner ideals we introduce the skeletons of an arbitrary monomial ideal I ⊂ S = K [ x 1 , …, x n ]. This allows us to compute the depth of S / I in terms of its skeleton ideals. We apply these techniques to show that Stanley's conjecture on Stanley decompositions of S / I holds provided it holds whenever S / I is Cohen–Macaulay. We also discuss a conjecture of Soleyman Jahan and show that it suffices to prove his conjecture for monomial ideals with linear resolution (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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