
Accession Number : AD0705612
Title : ON THE FOUNDATIONS OF COMBINATORIAL THEORY. IV. FINITE VECTOR SPACES AND EULERIAN GENERATING FUNCTIONS.
Descriptive Note : Technical rept.,
Corporate Author : HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS
Personal Author(s) : Goldman,Jay ; Rota,GianCarlo
Report Date : 17 APR 1970
Pagination or Media Count : 52
Abstract : The paper studies combinatorial aspects of the lattice of subspaces of a vector space over a finite field and its use in deriving classical and new qidentities. Set theoretic interpretations of these identities are given in terms of the enumeration of vector spaces and linear transformations. The incidence algebra of a partially ordered set is shown to be a true generalization of the notion of a generating function and Eulerian generating functions are applied to count a variety of vector space objects. Combinatorial interpretations are provided for general qdifference equations. (Author)
Descriptors : (*VECTOR SPACES, *COMBINATORIAL ANALYSIS), SET THEORY, NUMBER THEORY, IDENTITIES, POLYNOMIALS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE