Counting corners in partitions

Aubrey Blecher; Charlotte Brennan; Arnold Knopfmacher; Toufik Mansour

doi:10.1007/s11139-014-9666-4

Counting corners in partitions

Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-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 language	American English
Pages (from-to)	201-224
Number of pages	24
Journal	Ramanujan Journal
Volume	39
Issue number	1
DOIs	https://doi.org/10.1007/s11139-014-9666-4
State	Published - 1 Jan 2016

Keywords

Asymptotics
Corners
Generating functions
Partitions

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-014-9666-4

Cite this

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title = "Counting corners in partitions",

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.",

keywords = "Asymptotics, Corners, Generating functions, Partitions",

author = "Aubrey Blecher and Charlotte Brennan and Arnold Knopfmacher and Toufik Mansour",

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AU - Brennan, Charlotte

AU - Knopfmacher, Arnold

AU - Mansour, Toufik

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N2 - 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.

AB - 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.

KW - Asymptotics

KW - Corners

KW - Generating functions

KW - Partitions

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U2 - 10.1007/s11139-014-9666-4

DO - 10.1007/s11139-014-9666-4

M3 - Article

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VL - 39

SP - 201

EP - 224

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1

ER -

Counting corners in partitions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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