A combinatorial proof of the Rogers--Ramanujan and Schur identities

DOI10.1016/j.jcta.2005.09.007zbMath1094.05003arXivmath/0411072OpenAlexW2039325744MaRDI QIDQ2500615

Igor Pak, Cilanne E. Boulet

Publication date: 17 August 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411072

zbMATH Keywords

bijectioninteger partitionDyson's rankRogers-Ramanujan identitySchur's identity

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17)

Related Items (16)

Interview with Igor Pak ⋮ Refinements of the Rogers–Ramanujan Identities ⋮ Bilateral identities of the Rogers–Ramanujan type ⋮ Rogers-Ramanujan identities and the Robinson-Schensted-Knuth correspondence ⋮ The method of combinatorial telescoping ⋮ Partitions with part difference conditions and Bressoud's conjecture ⋮ Dyson's new symmetry and generalized Rogers-Ramanujan identities ⋮ Overpartitions, lattice paths, and Rogers-Ramanujan identities ⋮ Geometry and complexity of O'Hara's algorithm ⋮ ON THE SUM OF PARTS IN THE PARTITIONS OF n INTO DISTINCT PARTS ⋮ Legendre theorems for subclasses of overpartitions ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ A truncated theta identity of Gauss and overpartitions into odd parts ⋮ A bijective proof of a limiting case of Watson's \(_8\phi_7\) transformation formula ⋮ Distribution of the full rank in residue classes for odd moduli ⋮ Refinement for sequences in partitions

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• Generalized Rogers-Ramanujan bijections
• Some observations on Dyson's new symmetries of partitions
• Variants of the Rogers-Ramanujan identities
• On Fine's partition theorems, Dyson, Andrews, and missed opportunities
• Bijecting Euler's Partitions-Recurrence
• Partitions and Durfee Dissection
• An Enumerative Proof of An Identity of Jacobi
• Shorter Notes: A Simple Proof of Jacobi's Triple Product Identity
• A new symmetry of partitions
• Sieves in the Theory of Partitions

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