8 papers
On the nonnegativity of monomial immanants for hook partitions
Xiangshuai Dong, Tingzeng Wu, Xing Gao
Let be an real matrix and let be a partition of . Let be the class function dual to the Young permutation character, and let $$ ϕ^λ[A] = \sum_…
Solution to an open problem on the computational complexity of immanant
Xiangshuai Dong, Tingzeng Wu, Xing Gao
Immanants are a class of generalized matrix functions associated with the irreducible characters of the symmetric group. Bürgisser [SIAM J. Comput., 30 (2000), pp. 1023--1040] prov…
Disuccessors, Gröbner-Shirshov bases and free L-dendriform algebras
Huhu Zhang, Xing Gao, Yuanyuan Zhang
In this paper, we prove respectively that the disuccessor operations on the associative operad $\as$, the Lie operad $\lie$, and the pre-Lie operad $\prelie$ preserve Gröbner-Shirs…
Integro-differential rings on species and derived structures
Xing Gao, Li Guo, Markus Rosenkranz +2
In the theory of species, differential as well as integral operators are known to arise in a natural way. In this paper, we shall prove that they precisely fit together in the alge…
Averaging operators on groups and Hopf algebras
Huhu Zhang, Xing Gao
Rota-Baxter operators on groups were studied quite recently. Motivated mainly by the fact that weight zero Rota-Baxter operators and averaging operators are Koszul dual to each oth…
Weighted differential (-tri)dendriform algebras
Yuanyuan Zhang, Huhu Zhang, Tingzeng Wu +1
In this paper, we first introduce a weighted derivation on algebras over an operad , and prove that for the free -algebra, its weighted derivation is determined by…
Some new operated Lie polynomial identities and Gröbner-Shirshov bases
Huhu Zhang, Xing Gao, Tingzeng Wu +1
Bremner and Elgendy developed a classification of operated polynomial identities for linear operators on associative algebras, encompassing both classical and newly discovered case…
Compatible structures of operads by polarization, their Koszul duality and Manin products
Huhu Zhang, Xing Gao, Li Guo
Algebraic structures with multiple copies of a given type of operations interrelated by various compatibility conditions have long being studied in mathematics and mathematical phy…