Research Info

Home /Skeletons of monomial ideals
Title Skeletons of monomial ideals
Type JournalPaper
Keywords Monomial ideals;depth;skeleton;Cohen−Macaulay;Stanley decompositions
Abstract 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 [x1, …, xn ]. 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
Researchers Xinxian Zheng (Third Researcher), Ali Soleyman Jahan (Second Researcher), Jurgen Herzog (First Researcher)