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Partition bijections, a survey (Q851247)

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scientific article; zbMATH DE number 5073854

Language	Label	Description	Also known as
English	Partition bijections, a survey	scientific article; zbMATH DE number 5073854

Statements

scholarly article

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Partition bijections, a survey (English)

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The Ramanujan Journal

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publication date

17 November 2006

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zbMATH Keywords

integer partitions

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Young diagram

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bijection

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involution

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plane partitions

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involution principle

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\(q\)-series

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MaRDI profile type

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full work available at URL

https://doi.org/10.1007/s11139-006-9576-1

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Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series

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Addition and counting: The arithmetic of partitions

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Partition Identities--From Euler to the Present

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A variation on a theme of Sylvester -- a smoother road to Göllnitz's (Big) theorem

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Partition identities and a continued fraction of Ramanujan

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Schur's Partition Theorem, Companions, Refinements and Generalizations

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Shorter Notes: A Simple Proof of Jacobi's Triple Product Identity

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ON BASIC HYPERGEOMETRIC SERIES, MOCK THETA FUNCTIONS, AND PARTITIONS (II)

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On generalizations of Euler's partition theorem

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Enumerative proofs of certain <i>q</i>-identities

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On a calculus of partition functions

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Two theorems of Gauss and allied identities proved arithmetically

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An Extension of Carlitz's Bipartition Identity

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An Introduction to Ramanujan's "lost" Notebook

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A Note on Partitions and Triangles With Integer Sides

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Partitions and Durfee Dissection

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Ramanujan's ``lost'' notebook. I: Partial Theta-functions

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Some debts I owe

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MacMahon's partition analysis. II: Fundamental theorems

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A Short Proof of Jacobi's Formula for the Number of Representations of an Integer as a Sum of Four Squares

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Dyson’s crank of a partition

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The work of George Andrews: a Madison perspective.

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Some Properties of Partitions

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Hooks and powers of parts in partitions

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The form 𝑤𝑥+𝑥𝑦+𝑦𝑧+𝑧𝑢

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Enumeration of plane partitions

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Some observations on Dyson's new symmetries of partitions

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A bijection for Lebesgue's partition identity in the spirit of Sylvester

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On hooks of Young diagrams

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On pairs of partitions with steadily decreasing parts

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Lecture hall partitions

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A refinement of the lecture hall theorem

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On a partition theorem of Göllnitz.

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A Combinatorial Proof of Schur's 1926 Partition Theorem

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On Uchimura’s Connection between Partitions and the Number of Divisors

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A short Rogers-Ramanujan bijection

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Bijecting Euler's Partitions-Recurrence

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Generalized Rogers-Ramanujan bijections

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Random partitions with non-negative \(r\)th differences

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Some generating functions

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A Simple Proof of the Quintuple Product Identity

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Franklin's argument proves an identity of Zagier

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Vector Partitions and Combinatorial Identities

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PIE-sums: A combinatorial tool for partition theory

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Particle seas and basic hypergeometric series.

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Frobenius partitions and the combinatorics of Ramanujan's \(_{1}\psi_{1}\) summation

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A new symmetry of partitions

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Mappings and symmetries of partitions

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On an elementary proof of some asymptotic formulas in the theory of partitions

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Recurrences for the Sum of Divisors

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Theta constants, Riemann surfaces and the modular group. An introduction with applications to uniformization theorems, partition identities and combinatorial number theory

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Some New Results on Partitions

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The triple, quintuple and setuple product identities revisited

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Variants of the Rogers-Ramanujan identities

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A Rogers-Ramanujan bijection

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New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11

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Combinatorial proof of a theorem on partitions into an even or odd number of parts

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A Partition Identity of the Euler Type

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Simple proofs of identities of MacMahon and Jacobi

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Polynomial identities which imply identities of Euler and Jacobi

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A Simple Proof of Jacobi's Two-Square Theorem

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A Simple Proof of Jacobi's Four-Square Theorem

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An Involution of Blocks in the Partitions of n

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Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum

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An involution for Jacobi's identity

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A note on partitions into distinct parts and odd parts

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Another involution principle-free bijective proof of Stanley's hook-content formula

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A simple combinatorial method for proving Jacobi's identity and its generalizations

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A Combinatorial Proof of the Triple Product Identity

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An extension of Franklin's bijection

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Affine root systems and Dedekind's \(\eta\)-function

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Bijections for partition identities

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Partition identities and geometric bijections

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Hook length formula and geometric combinatorics

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A generalization of Sylvester's identity

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Bijective proofs of some classical partition identities

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Bijective proofs of certain vector partition identities

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A Short Proof of an Identity of Euler

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Two Enumerative Proofs of an Identity of Jacobi

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An identity for the divisor generating function arising from sorting theory

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Identically distributed pairs of partition statistics

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An Enumerative Proof of An Identity of Jacobi

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A One-Sentence Proof That Every Prime p≡1(\mod 4) Is a Sum of Two Squares

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The \(q\)-variations of Sylvester's bijection between odd and strict partitions

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A direct combinatorial proof of the Jacobi identity

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S11139-006-9576-1

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Sitelinks

Mathematics(1 entry)

mardi Publication:851247

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