Abstract
We introduce a class of ideals generated by a set of -minors of an -matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.
Citation
Viviana Ene. Jürgen Herzog. Takayuki Hibi. Ayesha Asloob Qureshi. "The binomial edge ideal of a pair of graphs." Nagoya Math. J. 213 105 - 125, March 2014. https://doi.org/10.1215/00277630-2389872
Information