2021/02/04 by Higashitani, Akihiro, Matsushita, Koji
#05C25 #13A02 #13F65 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13H10 #Secondary 52B20
paper · doi:10.48550/arxiv.2102.02349
Levelness and almost Gorensteinness are well-studied properties on graded rings as a generalized notion of Gorensteinness. In the present paper, we study those properties for the edge rings of the complete multipartite graphs, denoted by \Bbbk[Kr1,…,rn] with 1 ≤ r1 ≤ ⋯ ≤ rn. We give the complete characterization of which \Bbbk[Kr1,…,rn] is level in terms of n and r1,…,rn. Similarly, we also give the complete characterization of which \Bbbk[Kr1,…,rn] is almost Gorenstein in terms of n and r1,…,rn.