A Combinatorial Generalization of the Rogers-Ramanujan Identities
From MaRDI portal
Publication:3282052
DOI10.2307/2372962zbMath0100.27303OpenAlexW2024949453WikidataQ105723344 ScholiaQ105723344MaRDI QIDQ3282052
Publication date: 1961
Published in: American Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2372962
Elementary theory of partitions (11P81) Partition identities; identities of Rogers-Ramanujan type (11P84)
Related Items
ON MULTI-COLOR PARTITIONS AND THE GENERALIZED ROGERS–RAMANUJAN IDENTITIES ⋮ Asymmetric Rogers–Ramanujan type identities. I. The Andrews–Uncu conjecture ⋮ Bilateral identities of the Rogers–Ramanujan type ⋮ Separable integer partition classes ⋮ New proofs of some double sum Rogers-Ramanujan type identities ⋮ New companions to Gordon identities from commutative algebra ⋮ The 𝐴₂ Andrews–Gordon identities and cylindric partitions ⋮ Linked partition ideals and a family of quadruple summations ⋮ Modulo d extension of parity results in Rogers–Ramanujan–Gordon type overpartition identities ⋮ Unnamed Item ⋮ A Construction of the Level 3 Modules for the Affine Lie Algebra 𝐴₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type ⋮ A Generalization of the Classical Partition Theorems ⋮ Unnamed Item ⋮ On identities of the Rogers-Ramanujan type ⋮ Differences of Partition Functions: The Anti-telescoping Method ⋮ Some congruences modulo 2, 8 and 12 for Andrews' singular overpartitions ⋮ Parafermionic quasi-particle basis and fermionic-type characters ⋮ Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra $A^{(2)}_2$ ⋮ Bounded Littlewood identities ⋮ Unnamed Item ⋮ Cylindric partitions and some new $A_2$ Rogers–Ramanujan identities ⋮ New partition identities from \(C^{(1)}_\ell\)-modules ⋮ Linked partition ideals and the Alladi-Schur theorem ⋮ A solvable lattice model and related Rogers-Ramanujan type identities ⋮ On simplifications of certain \(q\)-multisums ⋮ Generalization of Dyson's rank and non-Rogers-Ramanujan partitions ⋮ Asymptotic analogs of the Rogers-Ramanujan identities ⋮ Bressoud style identities for regular partitions and overpartitions ⋮ A \(q\)-multisum identity arising from finite chain ring probabilities ⋮ Quasi-particles in the principal picture of 𝔰𝔩̂2 and Rogers–Ramanujan-type identities ⋮ Annihilating ideals of standard modules of \({\mathfrak sl}(2,{\mathbb{C}})^\sim\) and combinatorial identities ⋮ Lattice gas generalization of the hard hexagon model. I: Star-triangle relation and local densities ⋮ Lattice gas generalization of the hard hexagon model. II: The local densities as elliptic functions ⋮ Lattice gas generalization of the hard hexagon model. III: \(q\)-trinomial coefficients ⋮ Rogers-Ramanujan identities for n-color partitions ⋮ Generalisations of some theorems of Ramanujan ⋮ Density of free modules over finite chain rings ⋮ Ghost series and a motivated proof of the Andrews-Bressoud identities ⋮ Ramanujan-type partial theta identities and conjugate Bailey pairs. II: Multisums ⋮ A motivated proof of the Göllnitz-Gordon-Andrews identities ⋮ Continued fractions and fermionic representations for characters of \(M(p,p')\) minimal models ⋮ The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators ⋮ Combinatorial constructions of modules for infinite-dimensional Lie algebras. I: Principal subspace ⋮ Singular overpartitions ⋮ The Rogers-Ramanujan-Gordon identities, the generalized Göllnitz-Gordon identities, and parity questions ⋮ A motivated proof of Gordon's identities ⋮ Overpartitions and Bressoud's conjecture. I ⋮ Some sieves for partition theory ⋮ Hall-Littlewood polynomials and characters of affine Lie algebras ⋮ Extension of the partition sieve ⋮ Iteration process for multiple Rogers-Ramanujan identities ⋮ Parity in partition identities ⋮ Cluster parity indices of partitions ⋮ Linked partition ideals and Andrews-Gordon type series for Alladi and Gordon's extension of Schur's identity ⋮ Variations on a result of Bressoud ⋮ Bressoud's conjecture ⋮ IDENTITIES OF THE ROGERS–RAMANUJAN–SLATER TYPE ⋮ Leading terms of relations for standard modules of the affine Lie algebras \(C_n^{(1)}\) ⋮ A multilateral Bailey lemma and multiple Andrews-Gordon identities ⋮ Linked partition ideals, directed graphs and \(q\)-multi-summations ⋮ Andrews-Gordon type series for Capparelli's and Göllnitz-Gordon identities ⋮ Proofs and reductions of various conjectured partition identities of Kanade and Russell ⋮ A correspondence between partitions related to generalizations of the Rogers-Ramanujan identities ⋮ Multi-sum Rogers-Ramanujan type identities ⋮ Gordon's theorem for overpartitions. ⋮ New companions to the Andrews-Gordon identities motivated by commutative algebra ⋮ Rogers-Ramanujan identities and the Robinson-Schensted-Knuth correspondence ⋮ Anti-lecture Hall compositions and overpartitions ⋮ A Rogers-Ramanujan bijection ⋮ Ramanujan's ``lost notebook. III: The Rogers-Ramanujan continued fraction ⋮ New partition theoretic interpretations of Rogers-Ramanujan identities ⋮ A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities ⋮ A three-way correspondence between partitions ⋮ An extension to overpartitions of the Rogers-Ramanujan identities for even moduli ⋮ Ramanujan-Slater type identities related to the moduli 18 and 24 ⋮ Partitions with part difference conditions and Bressoud's conjecture ⋮ Overpartitions, lattice paths, and Rogers-Ramanujan identities ⋮ Overpartition pairs and two classes of basic hypergeometric series ⋮ Partition identities with mixed mock modular forms ⋮ An Andrews-Gordon type identity for overpartitions ⋮ Looking for a new version of Gordon's identities ⋮ Partition identities involving gaps and weights ⋮ Structure of certain level 2 standard modules for \(A_5^{(2)}\) and the Göllnitz-Gordon identities ⋮ A partition bijection related to the Rogers-Selberg identities and Gordon's theorem ⋮ The Bressoud-Göllnitz-Gordon theorem for overpartitions of even moduli ⋮ Basic series identities and combinatorics ⋮ An overpartition analogue of the Andrews-Göllnitz-Gordon theorem ⋮ An overpartition analogue of Bressoud's theorem of Rogers-Ramanujan-Gordon type ⋮ Andrews style partition identities ⋮ Random matrix theory over finite fields ⋮ Parity considerations in Andrews-Gordon identities ⋮ Srinivasa Ramanujan (1887‐1920) A centennial tribute ⋮ Andrews-Gordon type identities from combinations of Virasoro characters ⋮ A probabilistic proof of the Andrews--Gordon identities ⋮ Partially ordered sets and the Rogers-Ramanujan identities ⋮ A proof of Bressoud's conjecture related to the Rogers-Ramanujan identities ⋮ New weighted Rogers-Ramanujan partition theorems and their implications ⋮ Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities ⋮ A \(U(n+1)\) WP-Bailey lattice and its applications ⋮ A framework of Rogers-Ramanujan identities and their arithmetic properties ⋮ Hall-Littlewood Functions, Plane Partitions, and the Rogers-Ramanujan Identities ⋮ Combinatorial proofs and generalization of Bringmann, Lovejoy and Mahlburg's overpartition theorems ⋮ Polygonal numbers and Rogers-Ramanujan-Gordon theorem ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ Dyson's ``favorite identity and Chebyshev polynomials of the third and fourth kind ⋮ On the Alder Polynomials and a New Generalization of the Rogers-Ramanujan Identities ⋮ A generalization of the Rogers-Ramanujan identities for all moduli ⋮ Partition Theorems Related to Some Identities of Rogers and Watson ⋮ An analytic proof of the Borwein conjecture ⋮ Overpartition analogues for the generalized Rogers-Ramanujan identities of Bressoud ⋮ Partition identities ⋮ On self-conjugate split \(n\)-color partitions ⋮ Parity considerations in Rogers-Ramanujan-Gordon type overpartitions ⋮ Fermionic solution of the Andrews-Baxter-Forrester model. II: Proof of Melzer's polynomial identities. ⋮ False theta functions and companions to Capparelli's identities ⋮ On certain identities involving Nahm-type sums with double poles ⋮ The structure of standard modules. II: The case \(A_ 1^{(1)}\), principal gradation ⋮ An A₂ Bailey lemma and Rogers-Ramanujan-type identities ⋮ Even-odd partition identities of Rogers-Ramanujan type ⋮ Graded dimensions of principal subspaces and modular Andrews–Gordon-type series ⋮ Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities ⋮ On the work of Basil Gordon