THE NUMBER OF SUBSPACES OF A VECTOR SPACE.

Abstract

The number G sub n of subspaces of an n-dimensional vector space over GF(q) is studied by the symbolic calculus. This calculus provides a general technique for proving theorems in particular identities, involving the G sub n and the Gaussian coefficient (n, k). Examples include a recursion for the G sub n, an infinite product expansion for the Eulerian generating function of the G sub n, and a q-analog of the Pascal triangle for the (n, k). (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 28, 1969
Accession Number
AD0683687

Entities

People

  • Gian-carlo Rota
  • Jay Goldman

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Calculus
  • Coefficients
  • Cooperation
  • Identities
  • Massachusetts
  • Mathematics
  • Triangles
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers