This paper demonstrates that discrete polymatroids yield toric ideals generated by symmetric exchange binomials, suggesting implications for graph theory.
It has been conjectured that the toric ideal of the base ring of a discrete polymatroid is generated by symmetric exchange binomials. In the present paper, we give several classes of discrete polymatroids which yield toric ideals generated by symmetric exchange binomials. Especially, we are interested in the discrete polymatroids arising from bounded powers of edge ideals of finite graphs.
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Hibi et al. (2025) studied this question.
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