Bijective proofs of some classical partition identities

DOI10.1016/0097-3165(82)90040-1zbMath0491.05012OpenAlexW2064488687WikidataQ114215159 ScholiaQ114215159MaRDI QIDQ1167170

Jeffery B. Remmel

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0097-3165(82)90040-1

zbMATH Keywords

involution principle

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81)

Related Items (24)

Finding direct partition bijections by two-directional rewriting techniques ⋮ Combinatorial proofs and generalizations of conjectures related to Euler's partition theorem ⋮ The combinatorics of Jeff Remmel ⋮ Counting corners in partitions ⋮ Bijective proofs of basic hypergeometric series identities ⋮ Unnamed Item ⋮ Partition bijections, a survey ⋮ Bijections for partition identities ⋮ A class of lattices with Möbius function \(\pm 1,0\) ⋮ The two-way rewriting in action: removing the mystery of Euler-Glaisher's map ⋮ Probabilistic Divide-and-Conquer: A New Exact Simulation Method, With Integer Partitions as an Example ⋮ A Rogers-Ramanujan bijection ⋮ Multiset rewriting over Fibonacci and tribonacci numbers ⋮ Rook and Wilf equivalence of integer partitions ⋮ Complementary Schur asymptotics for partitions ⋮ A bijective proof of the generating function for the number of reverse plane partitions via lattice paths ⋮ Bijective matrix algebra ⋮ Geometry and complexity of O'Hara's algorithm ⋮ Gray code enumeration of families of integer partitions ⋮ Sieve-equivalence and explicit bijections ⋮ Sieve equivalence in generalized partition theory ⋮ Garsia and Milne's bijective proof of the inclusion-exclusion principle ⋮ A short Hook-lengths bijection inspired by the Greene-Nijenhuis-Wilf proof ⋮ Ultimate chromatic polynomials

Cites Work

• A bijective proof of the Hook formula for the number of column strict tableaux with bounded entries
• Some sieves for partition theory
• String overlaps, pattern matching, and nontransitive games
• PIE-sums: A combinatorial tool for partition theory
• A Rogers-Ramanujan bijection
• A bijective proof of the generating function for the number of reverse plane partitions via lattice paths
• A Combinatorial Proof of Schur's 1926 Partition Theorem
• Bijective proofs of formulae for the number of standard Yound tableaux
• On the Geometry of Numbers in Elementary Number Theory
• Two Theorems of Euler and a General Partition Theorem
• Partition Theorems for Euler Pairs
• Unnamed Item

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