2011/01/21 by Takayuki Hibi, Hibi, Takayuki, Akihiro Higashitani +5
Computer Science · Mathematics · Medicine · #13P10 #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1101.4058
openalex publication_date 2011/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite graph on the vertex set [d] = \1, ..., d \ with the edges e1, ..., en and K[\tb] = K[t1, ..., td] the polynomial ring in d variables over a field K. The edge ring of G is the semigroup ring K[G] which is generated by those monomials \tbe = titj such that e = \i, j\ is an edge of G. Let K[\xb] = K[x1, ..., xn] be the polynomial ring in n variables over K and define the surjective homomorphism π: K[\xb] → K[G] by setting π(xi) = \tbei for i = 1, ..., n. The toric ideal IG of G is the kernel of π. It will be proved that, given integers f and d with 6 ≤ f ≤ d, there exist a finite connected nonbipartite graph G on [d] together with a reverse lexicographic order