TL;DR
This paper investigates the structure of Betti cones generated by edge ideals, providing formulas for their dimensions and those of specific subcones, advancing understanding in algebraic combinatorics.
Contribution
It introduces a formula for the dimensions of Betti cones of edge ideals and their subcones based on height, a novel contribution to Boij-Söderberg theory.
Findings
Derived formulas for Betti cone dimensions
Calculated dimensions for subcones of specific heights
Enhanced understanding of Betti cone structure in edge ideals
Abstract
Boij-S\"{o}derberg Theory views the Betti diagrams of graded modules over polynomial rings as vectors in a rational vector space, and studies the cone that these vectors generate (called a 'Betti Cone'). The objects of study in this paper are the Betti cones generated by edge ideals; in particular this paper will present and prove a formula for the dimensions of these cones, and for the subcones generated by edge ideals of specific heights.
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