PROBLEMS IN PARTITION THEORY AND RELATED TOPICS

Abstract

The report falls into six sections together with five appendices. The first investigation studies rotatable partitions. In the second section a general identity involving xi-functions is found. The third section introduces a new combinatorial idea, the n-stack, gives generating functions for the number of n-stacks under certain restrictions and under no restrictions and finds asymptotic values for these numbers for large n. The fourth appendix is a short, semi-expository paper correcting a statement by another author that a particular problem in partition theory is unsolved. The fifth section finds necessary and sufficient conditions that almost all graphs of a given kind on n unlabelled nodes shall be connected. The sixth section reports preliminary investigation into the asymptotic expansions of, and relations between, the number of connected and disconnected graphs of a given kind on n labelled and on n unlabelled nodes when n is large.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1967
Accession Number
AD0665400

Entities

People

  • Edward M. Wright

Organizations

  • University of Aberdeen

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Asymptotic Series
  • Binomials
  • Coefficients
  • Complex Numbers
  • Contractors
  • Contracts
  • Graph Theory
  • Identities
  • Mathematics
  • Numbers
  • Polynomials
  • Power Series
  • Security
  • Sequences
  • Statistical Mechanics
  • United States

Fields of Study

  • Mathematics

Readers

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  • Operations Research
  • Technical Research and Report Writing.