Symbolic computation on the partition lattice of an n-set. (November 2019)

• Record Type: Journal Article
• Authors: Li, Yongbin; Fu, Qiuju; Deng, Renbin
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 185
• Page End: 201
• Publication Date: 2019-11
• Subjects: Gröbner basis -- Partition lattice -- Rank-generating function -- Characteristic polynomial; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.02.007
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, an injection from the partition lattice Π n to a zero-dimensional affine algebra over the finite field F 2 is constructed. We study some interesting properties of the injection and present two direct sum decompositions of the zero-dimensional affine algebra. Based upon these, some properties of Π n are revealed in an algebraic manner, for instance, the rank-generating function and characteristic polynomial of Π n can be derived using the symbolic method.