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Limit Shapes via Bijections

Part of: Limit theorems Combinatorial probability Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  02 August 2018

STEPHEN DeSALVO  and
IGOR PAK
STEPHEN DeSALVO
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail: stephendesalvo@math.ucla.edu, pak@math.ucla.edu)
IGOR PAK
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail: stephendesalvo@math.ucla.edu, pak@math.ucla.edu)
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Abstract

We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes continuously in the plane. We start with bijections outlined in [43], and extend them to include limit shapes with different scaling functions.

MSC classification

Primary: 05A17: Partitions of integers
Secondary: 05A19: Combinatorial identities, bijective combinatorics 60C05: Combinatorial probability 11P82: Analytic theory of partitions 11P84: Partition identities; identities of Rogers-Ramanujan type 60F10: Large deviations

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Issue 2 , March 2019 , pp. 187 - 240
Copyright
Copyright © Cambridge University Press 2018 

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