Counting corners in partitions

Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Research output: Contribution to journalArticlepeer-review

Abstract

A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. It may be represented by a Ferrers diagram. These diagrams contain corners which are points of degree two. We define corners of types (a,b), (a+b) and (a+,b+), and also define the size of a corner. Via a generating function, we count corners of each type and corners of size $$m$$m. We also find asymptotics for the number of corners as n tends to infinity.

Original languageEnglish
Pages (from-to)201-224
Number of pages24
JournalRamanujan Journal
Volume39
Issue number1
DOIs
StatePublished - 1 Jan 2016

Bibliographical note

Funding Information:
Charlotte Brennan and Arnold Knopfmacher were supported by the National Research Foundation under Grant Numbers 86329 and 81021, respectively.

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Keywords

  • Asymptotics
  • Corners
  • Generating functions
  • Partitions

ASJC Scopus subject areas

  • Algebra and Number Theory

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