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has been cited by the following article:

• TITLE: Algebra and Coalgebra on Posets

  AUTHORS: Rongrong Yuan, Huilan Li

  KEYWORDS: Conjunction Product, Unshuffle Coproduct, Poset, Graded, Free

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.7, July 19, 2022

  ABSTRACT: 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.