The number of direct-sum decompositions of a finite vector space

Publication date: 22 March 2016

Abstract: The theory of q-analogs develops many combinatorial formulas for finite vector spaces over a finite field with q elements--all in analogy with formulas for finite sets (which are the special case of q=1). A direct-sum decomposition of a finite vector space is the vector space analogue of a set partition. This paper develops the formulas for the number of direct-sum decompositions that are the q-analogs of the formulas for: (1) the number of set partitions with a given number partition signature; (2) the number of set partitions of an n-element set with m blocks (the Stirling numbers of the second kind); and (3) for the total number of set partitions of an n-element set (the Bell numbers).

Mathematics Subject Classification ID

Partitions of sets (05A18)

This page was built for publication: The number of direct-sum decompositions of a finite vector space

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6271836)