Results 31 to 40 of about 505,867 (109)
On a generalized basic series and Rogers-Ramanujan type identities [PDF]
, 2023 In this paper, we give the generalization of MacMahon\u27s type combinatorial identities. A generalized $q$-series is interpreted as the generating function of two different combinatorial objects, viz., restricted $n$-color partitions and weighted ...
Ranganatha, D. +2 more
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New Proofs of Some q‐Summation and q‐Transformation Formulas
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q‐series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.
Xian-Fang Liu +3 more
wiley +1 more source
Revisiting a Classic Identity That Implies the Rogers–Ramanujan Identities III
MathematicsThis is the third installment in a series of papers on a one-parameter extension of the Rogers–Ramanujan identities (this extension was discovered independently by Rogers and Ramanujan). In this paper, we report a new proof of this identity.
Hei-Chi Chan
doaj +1 more source
New Partition Theoretic Interpretations of Rogers‐Ramanujan Identities
International Journal of Combinatorics, Volume 2012, Issue 1, 2012., 2012 The generating function for a restricted partition function is derived. This in conjunction with two identities of Rogers provides new partition theoretic interpretations of Rogers‐Ramanujan identities.
A. K. Agarwal, M. Goyal, Toufik Mansour
wiley +1 more source
New Finite Rogers-Ramanujan Identities
, 2009 19 pages.International audienceWe present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson's transformation formula by specialization or through Bailey's method, the second ...
Jouhet, Frederic +2 more
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Erdős‐Rogers Functions for Arbitrary Pairs of Graphs
Random Structures &Algorithms, Volume 68, Issue 3, May 2026.ABSTRACT Let fF,G(n)$$ {f}_{F,G}(n) $$ be the largest size of an induced F$$ F $$‐free subgraph that every n$$ n $$‐vertex G$$ G $$‐free graph is guaranteed to contain. We prove that for any triangle‐free graph F$$ F $$, fF,K3(n)=fK2,K3(n)1+o(1)=n12+o(1).$$ {f}_{F,{K}_3}(n)={f}_{K_2,{K}_3}{(n)}^{1+o(1)}={n}^{\frac{1}{2}+o(1)}. $$Along the way we give a
Dhruv Mubayi, Jacques Verstraëte
wiley +1 more source
Modular Identities and Explicit Evaluations of a Continued Fraction of Ramanujan
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We study a new continued fraction of Ramanujan. We prove its modular identities and give some explicit evaluations.
Nipen Saikia, Stefaan Caenepeel
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Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract In the first paper of this series, we gave infinite families of coloured partition identities which generalise Primc's and Capparelli's classical identities. In this second paper, we study the representation theoretic consequences of our combinatorial results.
Jehanne Dousse, Isaac Konan
wiley +1 more source
A Parameter for Ramanujan′s Function χ(q): Its Explicit Values and Applications
International Scholarly Research Notices, Volume 2012, Issue 1, 2012., 2012 We define a new parameter Ik,n involving quotient of Ramanujan′s function χ(q) for positive real numbers k and n and study its several properties. We prove some general theorems for the explicit evaluations of the parameter Ik,n and find many explicit values.
Nipen Saikia +3 more
wiley +1 more source
Certain Transformation Formulae for Polybasic Hypergeometric Series
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Making use of Bailey′s transformation and certain known summations of truncated series, an attempt has been made to establish transformation formulae involving polybasic hypergeometric series.
Pankaj Srivastava +4 more
wiley +1 more source