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, pp. 1-23) and results given by Santos (Computer algebra and identities of the Rogers-Ramanujan type. ... Thesis, Pennsylvania State University, 1991) we give a polynomial generalization for the Fibonacci sequence from which we get new formula and combinatorial interpretation for the Fibonacci numbers. ... Acknowledgements We are grateful to George Andrews for important suggestions regarding the use of the Frobenius Symbol. ...doi:10.1016/s0012-365x(01)00378-8 fatcat:6n6pkbwzhjdzbaa32n5gr5vh4a
This determinant identity gives rise to new polynomial generalizations of known Rogers-Ramanujan type identities. Several examples of new Rogers-Ramanujan type identities are given. ... We give a combinatorial proof of a general determinant identity for associated polynomials. ... In Section 4, we will give an analagous lattice path proof of a polynomial identity related to our main theorem and state some new generalizations of known Rogers-Ramanujan type identities. ...doi:10.37236/1932 fatcat:d7macgj5wvdrdnmnzu6s3b5uwa
We provide finite analogs of a pair of two-variable $q$-series identities from Ramanujan's lost notebook and a companion identity. ... Acknowledgments Many thanks to Doron Zeilberger for revolutionizing the way we approach the discovery and proof of identities, especially those of the hypergeometric and q-hypergeometric type. ... We also thank the anonymous referee for catching a number of typographical errors and pointing out some details that needed clarification. ...doi:10.37236/2011 fatcat:gsjo57i2mbhireknjrqa65zp6e
In this paper a new polynomial analogue of the Rogers-Ramanujan identities is proven. Here the product is replaced by a partial theta series and the sum by a weighted sum over the Schur polynomials. ... The famous Rogers-Ramanujan identities are q-series identities equating a sum and a product. ...
By “finite analogue” of a Rogers-Ramanujan-type identity we mean an identity between two terminating q-series (which may be multisums), which, in the limit, becomes the Rogers-Ramanujan identity if we ... “method” which, given a Rogers-Ramanujan-type identity, finds a finite analogue for it. ...
technique for proving identities of the Rogers-Ramanujan type. ... There are numerous published proofs of the celebrated Rogers- Ramanujan identities: 1 (1 a gt!) ...
There are various connections between symmetric functions and identities of the Rogers-Ramanujan type. For instance, J. R. Stem- bridge [Trans. Amer. Math. ... Soc. 319 (1990), no. 2, 469-498; MR 90j:05021] derived the Rogers-Ramanujan identities by using prop- erties of the Hall-Littlewood polynomials [I. G. ...
The basic idea of this paper is to show how to derive identities of Rogers-Ramanujan type from L. Carlitz’s inversion formula [Duke. Math. ... This idea is not new since Andrews, Gessel and Stanton have already used this approach to prove identities of 33E Other special functions 96i:33035 Rogers-Ramanujan type. ...
—g/X, 939) oo (qx*,.4/X7397 oo Mizan Rahman (3-CARL; Ottawa, ON) 2003f:33023 33D15 11B65 Rajkhowa, Pranjal (6-COTT; Guwahati) Further new identities of the Rogers-Ramanujan type. ... Using Bailey’s lemma and basic hypergeometric series transfor- mations the author derives some further q-identities of Rogers- Ramanujan type. ...
New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. ... These include a very short proof of the first Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping. ... Acknowledgment: The author thanks Volker Strehl, Herb Wilf and Doron Zeilberger for valuable suggestions and comments. ...doi:10.37236/1190 fatcat:yktph27vxnhybb5v2o62zu5gaa
Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan Identities. The linking object is the Hilbert-Poincaré series of the arc space over a point of the base variety. ... In the case of the double point this is precisely the generating series for the integer partitions without equal or consecutive parts. Résumé. ... = 0 in one variable y), thus retrieving the Rogers-Ramanujan identities. ...doi:10.1007/s11139-012-9401-y fatcat:r6f7pk6r5bfjtewa4v43k3apia
Phys. 83 (1996), no. 5-6, 795-837; MR 97i:82034], the authors be- gan a study of Rogers-Ramanujan-type identities for the characters of the N = | superconformal models SM(2,4v). ... P.| (BR-ECPM; Campinas) Rogers-Ramanujan type identities for partitions with attached odd parts. (English summary) Ramanujan J. 1 (1997), no. 1, 91-99. ...
Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. ... Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. ... I am also grateful to Alexander Berkovich, Paul Eakin, Peter Paule, Avinash Sathaye, and Doron Zeilberger for their support and encouragement of this project. ...doi:10.37236/1706 fatcat:rullk6akp5gqxh65n3fnxj2ejq
Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. ... Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. ... I am also grateful to Alexander Berkovich, Paul Eakin, Peter Paule, Avinash Sathaye, and Doron Zeilberger for for their support and encouragement of this project. ...arXiv:1901.02435v1 fatcat:kxicot3vkjfsth464tuzun7eum
in the Rogers-Ramanujan identities. ... However, the authors note (Conjecture 4.2) that equation (6) (called by them “the abstract RR identity for V”) should cover several infinite families of Rogers-Ramanujan type identities given previously ...
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