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,Gian-Carlo

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 q-identities. 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 q-difference equations. (Author)

Descriptors :   (*VECTOR SPACES, *COMBINATORIAL ANALYSIS), SET THEORY, NUMBER THEORY, IDENTITIES, POLYNOMIALS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE