12 citations · 119 across the 39 of their papers we have counts for
5 papers · 1 filter
Classification of 2-extendable bipartite and cubic non-bipartite vertex-transitive graphs
Qiuli Li, Xing Gao
In \cite{Chan95}, the authors classified the 2-extendable abelian Cayley graphs and posed the problem of characterizing all 2-extendable Cayley graphs. We first show that a connect…
Hopf algebras of rooted forests, cocyles and free Rota-Baxter algebras
Xing Gao, Li Guo, Tianjie Zhang
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum fie…
Bialgebra and Hopf algebra structures on free Rota-Baxter algebras
Xing Gao, Li Guo, Tianjie Zhang
In this paper, we obtain a canonical factorization of basis elements in free Rota-Baxter algebras built on bracketed words. This canonical factorization is applied to give a coalge…
Rota's Classification Problem, rewriting systems and Gröbner-Shirshov bases
Xing Gao, Li Guo
In this paper we revisit Rota's Classification Problem on classifying algebraic identities for linear operator. We reformulate Rota's Classification Problem in the contexts of rewr…
Averaging algebras, rewriting systems and Grbner-Shirshov bases
Xing Gao, Tianjie Zhang
In this paper, we study the averaging operator by assigning a rewriting system to it. We obtain some basic results on the kind of rewriting system we used. In particular, we obtain…