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- Title
Algebraic properties of the binomial edge ideal of a complete bipartite graph.
- Authors
Schenzel, Peter; Zafar, Sohail
- Abstract
Let JG denote the binomial edge ideal of a connected undirected graph on n vertices. This is the ideal generated by the binomials xiyj − xjyi, 1 ≤ i < j≤ n, in the polynomial ring S = K[ x1, . . . , xn, y1, . . . , yn] where { i, j} is an edge of G. We study the arithmetic properties of S/JG for G, the complete bipartite graph. In particular we compute dimensions, depths, Castelnuovo-Mumford regularities, Hilbert functions and multiplicities of them. As main results we give an explicit description of the modules of deficiencies, the duals of local cohomology modules, and prove the purity of the minimal free resolution of S/JG.
- Subjects
BINOMIAL equations; BIPARTITE graphs; GEOMETRIC vertices; FREE resolutions (Algebra); POLYNOMIAL rings; HILBERT functions
- Publication
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014, Vol 22, Issue 2, p217
- ISSN
1224-1784
- Publication type
Article
- DOI
10.2478/auom-2014-0043