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The binomial edge ideal of a pair of graphs

Published online by Cambridge University Press:  11 January 2016

Viviana Ene ,
Jürgen Herzog ,
Takayuki Hibi  and
Ayesha Asloob Qureshi
Viviana Ene
Affiliation:
Faculty of Mathematics and Computer Science Ovidius University, 900527 Constanta, Romania, vivian@univ-ovidius.ro
Jürgen Herzog
Affiliation:
Fachbereich Mathematik Universität Duisburg-Essen, Campus Essen 45117 Essen, Germany, juergen.herzog@uni-essen.de
Takayuki Hibi
Affiliation:
Department of Pure and Applied Mathematics Graduate School of Information Science and Technology Osaka University, Toyonaka Osaka 560-0043, Japan, hibi@math.sci.osaka-u.ac.jp
Ayesha Asloob Qureshi
Affiliation:
Abdus Salam School of Mathematical Sciences GC University, New Muslim Town Lahore 54600, Pakistan, ayesqi@gmail.com
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Abstract

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We introduce a class of ideals generated by a set of 2-minors of an (m × n)-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.

Keywords

13P1013C1313C1513P25

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 213 , March 2014 , pp. 105 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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