A unification of two refinements of Euler’s partition theorem

Chen, William Y. C.; Gao, Henry Y.; Ji, Kathy Q.; Li, Martin Y. X.

doi:10.1007/s11139-008-9156-7

Ramanujan J

2010

DOI: 10.1007/s11139-008-9156-7

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A unification of two refinements of Euler’s partition theorem

William Y. C. Chen

Henry Y. Gao

Kathy Q. Ji

et al.

Abstract: Abstract. We obtain a unification of two refinements of Euler's partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt's insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.

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Cited by 10 publications

References 17 publications

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A Lecture Hall Theorem for $${\varvec{m}}$$-Falling Partitions

Tang

Yee

2019

Ann. Comb.

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For an integer m ě 2, a partition λ " pλ1, λ2, . . .q is called m-falling, a notion introduced by Keith, if the least nonnegative residues mod m of λi's form a nonincreasing sequence. We extend a bijection originally due to the third author to deduce a lecture hall theorem for such m-falling partitions. A special case of this result gives rise to a finite version of Pak-Postnikov's pm, cq-generalization of Euler's theorem. Our work is partially motivated by a recent extension of Euler's theorem for all moduli, due to Keith and Xiong. We note that their result actually can be refined with one more parameter.

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A Lecture Hall Theorem for $${\varvec{m}}$$-Falling Partitions

Tang

Yee

2019

Ann. Comb.

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A Multiparameter Refinement of Euler’s Theorem

Wang,

Zhang

2024

Ann. Comb.

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Euler’s partition theorem for all moduli and new companions to Rogers–Ramanujan–Andrews–Gordon identities

Xiong

Keith

2019

Ramanujan J

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A unification of two refinements of Euler’s partition theorem

Abstract: Abstract. We obtain a unification of two refinements of Euler's partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt's insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.

Cited by 10 publications

References 17 publications

A Lecture Hall Theorem for $${\varvec{m}}$$-Falling Partitions

A Lecture Hall Theorem for $${\varvec{m}}$$-Falling Partitions

A Multiparameter Refinement of Euler’s Theorem

Euler’s partition theorem for all moduli and new companions to Rogers–Ramanujan–Andrews–Gordon identities

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