查看更多>>摘要：Let A be a finite-dimensional algebra over the real number field.We prove that the repetitive algebra A admits the dichotomy property of representation type,i.e.,A is either of discrete representation type or of strongly unbounded type.
查看更多>>摘要：In a Cohen-Macaulay local ring(A,m),we study the Hilbert function of an integrally closed m-primary ideal I whose reduction number is three.With a mild assump-tion we give an inequality ℓA(A/I)≥ e0(I)-e1(I)+(e2(I)+ℓA(I2/QI))/2,where ei(I)denotes the ith Hilbert coefficient and Q denotes a minimal reduction of I.The inequality is located between inequalities of Itoh and Elias-Valla.Furthermore,this inequality be-comes an equality if and only if the depth of the associated graded ring of I is larger than or equal to dim A-1.We also study the Cohen-Macaulayness of the associated graded rings of determinantal rings.
查看更多>>摘要：We introduce first the spanning simplicial complex(SSC)of a multigraph G,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs Urn,m with n edges including r multiple edges within and outside the cycle of length m,which are then used to compute the f-vector and Hilbert series of face ring k[Δs(Urn,m)]for the SSC Δ8(Urn,m).Moreover,we find the associated primes of the facet ideal IF(Δs(Urn,m)).Finally,we device a formula for homology groups of Δs(Urn,m)and prove that the SSC of a family of uni-cyclic multigraphs is Cohen-Macaulay.
查看更多>>摘要：The distance matrix of a connected graph G,denoted by D(G),is the matrix whose rows and columns are indexed by the vertex set V(G)such that the(vi,Vj)-entry is d(vi,Vj),where Vi,Vj ∈ V(G).The distance signature sig(D(G))of G is the inertia of D(G).In this paper,we determine the distance signature of the extended(co-extended)incidence graph of an affine design.Furthermore,we state that an open Graffiti conjecture is true for the extended(co-extended)incidence graphs of affine designs by investigating the lower bound of the matching number.
查看更多>>摘要：In this paper we present two new families of 2-(v,k,λ)designs with a flag-transitive and point-primitive automorphism group of product action type.More sur-prisingly,one of them is still a family of 2-(v,k,λ)designs with a flag-transitive and point-imprimitive automorphism group.
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