Linear strands of powers of certain binomial edge ideals
Abstract
We provide a closed formula for the graded Betti numbers in the linear strands of all powers of binomial edge ideals JG arising from closed graphs G that do not have the complete graph K4 as an induced subgraph. We show that these agree with the corresponding Betti numbers for the powers of the lexicographic initial ideal of JG, thereby confirming a conjecture of Ene--Rinaldo--Terai in a special case.
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