Symbolic computation on the partition lattice of an n-set. (November 2019) - Li, Yongbin; Fu, Qiuju; Deng, Renbin
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.