摘要
A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. Firstly, by associativity and the unitary property, we prove that the vector space with the conjunction product is a graded algebra. Then by the definition of free algebra, we prove that the algebra is free. Finally, by the coassociativity and the counitary property, we prove that the vector space with the unshuffle coproduct is a graded coalgebra.
A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. Firstly, by associativity and the unitary property, we prove that the vector space with the conjunction product is a graded algebra. Then by the definition of free algebra, we prove that the algebra is free. Finally, by the coassociativity and the counitary property, we prove that the vector space with the unshuffle coproduct is a graded coalgebra.
作者
Rongrong Yuan
Huilan Li
Rongrong Yuan;Huilan Li(School of Mathematics and Statistics, Shandong Normal University, Jinan, China)
