12 citations · 119 across the 39 of their papers we have counts for
9 papers · 1 filter
A Hopf algebra on subgraphs of a graph
Xiaomeng Wang, Shoujun Xu, Xing Gao
In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic st…
Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles
Yi Zhang, Dan Chen, Xing Gao +1
In this paper, we define a new coproduct on the space of decorated planar rooted forests to equip it with a weighted infinitesimal unitary bialgebraic structure. We introduce the c…
Weighted infinitesimal unitary bialgebras on matrix algebras and weighted associative Yang-Baxter equations
Yi Zhang, Xing Gao, Jia-wen Zheng
We equip a matrix algebra with a weighted infinitesimal unitary bialgebraic structure, via a construction of a suitable coproduct. Furthermore, an infinitesimal unitary Hopf algebr…
Hamiltonian decomposition of the Cayley graph on the dihedral group where is a prime
Hui Zhou, Liufeng Xu, Yang Cui +4
In this note, we give the Hamiltonian decomposition of the Cayley graph on the dihedral group where is a prime.
Infinitesimal unitary Hopf algebras and planar rooted forests
Xing Gao, Xiaomeng Wang
Infinitesimal bialgebras were introduced by Joni and Rota. An infinitesimal bialgebra is at the same time an algebra and coalgebra, in such a way that the comultiplication is a der…
Weighted infinitesimal bialgebras
Xing Gao, Yi Zhang
As an algebraic meaning of the nonhomogenous associative Yang-Baxter equation, weighted infinitesimal bialgebras play an important role in mathematics and mathematical physics. In…
Left counital Hopf algebras on free Nijenhuis algebras
Xing Gao, Peng Lei, Tianjie Zhang
Factorization in algebra is an important problem. In this paper, we first obtain a unique factorization in free Nijenhuis algebras. By using of this unique factorization, we then d…
Free operated monoids and Rewriting systems
Xing Gao, Jin Zhang
The construction of bases for quotients is an important problem. In this paper, applying the method of rewriting systems, we give a unified approach to construct sections---an alte…
Commutative modified Rota-Baxter algebras, shuffle products and Hopf algebras
Xigou Zhang, Xing Gao, Li Guo
In this paper, we begin a systematic study of modified Rota-Baxter algebras, as an associative analogue of the modified classical Yang-Baxter equation. We construct free commutativ…