Corpus ID: 236881349

Three families of toric rings arising from posets or graphs with small class groups

  title={Three families of toric rings arising from posets or graphs with small class groups},
  author={Akihiro Higashitani and Koji Matsushita},
The main objects of the present paper are (i) Hibi rings (toric rings arising from order polytopes of posets), (ii) stable set rings (toric rings arising from stable set polytopes of perfect graphs), and (iii) edge rings (toric rings arising from edge polytopes of graphs satisfying the odd cycle condition). The goal of the present paper is to analyze those three toric rings and to discuss their structures in the case where their class groups have small rank. We prove that the class groups of (i… Expand

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