A Stanley–Elder theorem on Cranks and Frobenius symbols

George E. Andrews; Manosij G. Dastidar; Thomas Morrill

doi:10.1007/s40993-021-00285-7

A Stanley–Elder theorem on Cranks and Frobenius symbols

George E. Andrews, Manosij G. Dastidar, Thomas Morrill

Mathematics

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2 Scopus citations

Abstract

The Stanley–Elder theorem asserts that the number of j’s in the partitions of n is equal to the number of parts that appear at least j times in a given partition of n, summed over all partitions of n. In this paper, we prove that the number of partitions of n with crank > j equals to half the total number of j’s in the Frobenius symbols for n.

Original language	English (US)
Article number	56
Journal	Research in Number Theory
Volume	7
Issue number	3
DOIs	https://doi.org/10.1007/s40993-021-00285-7
State	Published - Sep 2021

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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title = "A Stanley–Elder theorem on Cranks and Frobenius symbols",

abstract = "The Stanley–Elder theorem asserts that the number of j{\textquoteright}s in the partitions of n is equal to the number of parts that appear at least j times in a given partition of n, summed over all partitions of n. In this paper, we prove that the number of partitions of n with crank > j equals to half the total number of j{\textquoteright}s in the Frobenius symbols for n.",

author = "Andrews, {George E.} and Dastidar, {Manosij G.} and Thomas Morrill",

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A Stanley–Elder theorem on Cranks and Frobenius symbols

Abstract

All Science Journal Classification (ASJC) codes

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