MacMahon's Partition Analysis XIV: Partitions with n copies of n

George E. Andrews; Peter Paule

MacMahon's Partition Analysis XIV: Partitions with n copies of n

George E. Andrews, Peter Paule

Research Institute for Symbolic Computation

Research output: Working paper and reports › Preprint

Abstract

We apply the methods of partition analysis to partitions with~$n$ copies of~$n$. This allows us to obtain multivariable generating functions related to classical Rogers-Ramanujan type identities. Also, partitions with $n$ copies of $n$ are extended to partition diamonds yielding numerous new results including a natural connection to overpartitions and a variety of partition congruences.

Original language	English
Place of Publication	Linz, Hagenberg
Publisher	RISC, JKU
Number of pages	30
Publication status	Published - Oct 2022

Publication series

Name	RISC Report Series
No.	22-14

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Digital Transformation

Cite this

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AB - We apply the methods of partition analysis to partitions with~$n$ copies of~$n$. This allows us to obtain multivariable generating functions related to classical Rogers-Ramanujan type identities. Also, partitions with $n$ copies of $n$ are extended to partition diamonds yielding numerous new results including a natural connection to overpartitions and a variety of partition congruences.

M3 - Preprint

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