Koszul Bipartite Graphs
Copyright policy ) Takayuki Hibi; Hidefumi Ohsugi;
Koszul Bipartite Graphs
Let \(R = K[t_1, \ldots , t_d]\) be the polynomial ring in \(d\) indeterminates over a field \(K\). If \(G\) is a bipartite graph on the vertex set \(\{ 1, \ldots , d \}\), define \(K[G]\) to be the subalgebra of \(R\) generated by all monomials \(t_i t_j\) such that \(\{ i,j \}\) is an edge of \(G\). It is shown that if every \(n\)-cycle \((n \geq 6)\) has a chord, then \(K[G]\) is Koszul.
- Osaka University Japan
Graphs and linear algebra (matrices, eigenvalues, etc.), Applied Mathematics, bipartite graph, Paths and cycles, Koszul algebra
Graphs and linear algebra (matrices, eigenvalues, etc.), Applied Mathematics, bipartite graph, Paths and cycles, Koszul algebra
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).49 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
citations
Citations provided by BIP!
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Citations provided by BIP!popularityPopularity provided by BIP!
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
Popularity provided by BIP! 49
Top 10%
Top 1%
Average
hybrid
Fields of Science