ON THE FOUNDATIONS OF COMBINATORIAL THEORY. IV. FINITE VECTOR SPACES AND EULERIAN GENERATING FUNCTIONS.

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)

Document Details

Document Type
Technical Report
Publication Date
Apr 17, 1970
Accession Number
AD0705612

Entities

People

  • Gian-carlo Rota
  • Jay Goldman

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Difference Equations
  • Differential Equations
  • Equations
  • Identities
  • Mathematical Analysis
  • Mathematics
  • Real Variables
  • Space Objects
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space