Boij-S\"{o}derberg Decompositions of Lex-segment Ideals
Sema Gunturkun
TL;DR
This paper investigates the Boij-S"oderberg decompositions of Betti diagrams specifically for lex-segment ideals, providing explicit descriptions in terms of related lex-segment ideals.
Contribution
It offers a new explicit description of Boij-S"oderberg decompositions for lex-segment ideals based on related ideals, advancing understanding in this area.
Findings
Explicit Boij-S"oderberg decompositions for lex-segment ideals
Decomposition expressed via related lex-segment ideals
Enhanced understanding of Betti diagram structures
Abstract
Boij-S\"oderberg theory describes the scalar multiples of Betti diagrams of graded modules over a polynomial ring as a linear combination of pure diagrams with positive coefficients. There are a few results that describe Boij-S\"oderberg decompositions explicitly. In this paper, we focus on the Betti diagrams of lex-segment ideals and describe the Boij-S\"oderberg decomposition of a lex-segment ideal in terms of Boij-S\"oderberg decompositions of some other related lex-segment ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models