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):

Report Date:

1970-04-17

Pagination or Media Count:

52.0

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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE