COMBINATORIAL CONDITION FOR LINEARITY IN THE FIRST STEPS OF RESOLUTION OF MONOMIAL IDEALS
Subject Areas : Statistics
siamak yassemi
1
(‎School of Mathematics‎, ‎Statistics and Computer Science‎,
‎‎‎College of Science‎, ‎University of Tehran‎,‎Tehran‎, ‎Iran)
seyed abbas seyed mirzaei
2
(SCIENCE AND RESEARCH BRANCH, ISLAMIC AZAD UNIVERSITY (IAU), TEHRAN, IRAN)
Keywords: مجتمع های سادکی (d, r) -وتری, مجتمع های سادکی d -بعدی, تحلیل خطی, ایده ال استنلی – ریزنر,
Abstract :
There has been many researches in the field of combinational commutative algebra; however, what makes this research distinct from the previous ones is its focus on monomial ideals and their connection to graphs. The present study aims at various goals one of which is analyzing the existence of linear resolution of such ideals. Concerning combinatorial commutative algebra there are numerous methods for creating connection between combinational objects and algebric objects. This article is to study such objects through corresponding monomial ideals with graphs and simplicial complexes. The most significant treatable ideals of simplicial complex include edge ideal and Stanly-Reisner ideal. Let r be a positive integer. A monomial ideal I is said to be linear in the first r steps, if for some integer d , β_(i.i+j) (I)=0 for all 0≤i
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