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On the combinatorics of polynomial generalizations of Rogers–Ramanujan-type identities

2002
*
Discrete Mathematics
*

, pp. 1-23) and results given by Santos (Computer algebra and

doi:10.1016/s0012-365x(01)00378-8
fatcat:6n6pkbwzhjdzbaa32n5gr5vh4a
*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. ...##
###
A Determinant Identity that Implies Rogers-Ramanujan

2005
*
Electronic Journal of Combinatorics
*

This determinant

doi:10.37236/1932
fatcat:d7macgj5wvdrdnmnzu6s3b5uwa
*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*. ...##
###
Polynomial Generalizations of Two-Variable Ramanujan Type Identities

2011
*
Electronic Journal of Combinatorics
*

We provide finite analogs

doi:10.37236/2011
fatcat:gsjo57i2mbhireknjrqa65zp6e
*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. ...##
###
Page 2518 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

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. ...##
###
Page 6907 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

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. ...##
###
Page 2414 of Mathematical Reviews Vol. , Issue 91E
[page]

1991
*
Mathematical Reviews
*

technique for proving

*identities**of**the**Rogers*-*Ramanujan**type*. ... There are numerous published proofs*of**the*celebrated*Rogers*-*Ramanujan**identities*: 1 (1 a gt!) ...##
###
Page 5335 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

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. ...##
###
Page 5319 of Mathematical Reviews Vol. , Issue 96i
[page]

1996
*
Mathematical Reviews
*

*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*. ...

##
###
Page 4215 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

—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*. ...##
###
Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type

1994
*
Electronic Journal of Combinatorics
*

New short and easy computer proofs

doi:10.37236/1190
fatcat:yktph27vxnhybb5v2o62zu5gaa
*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. ...##
###
Arc spaces and the Rogers–Ramanujan identities

2012
*
The Ramanujan journal
*

Exploiting these relations we obtain a new approach to

doi:10.1007/s11139-012-9401-y
fatcat:r6f7pk6r5bfjtewa4v43k3apia
*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*. ...##
###
Page 6807 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

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. ...##
###
Finite Rogers-Ramanujan Type Identities

2003
*
Electronic Journal of Combinatorics
*

*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. ...

##
###
Finite Rogers--Ramanujan type identities
[article]

2019
*
arXiv
*
pre-print

*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. ...

##
###
Page 1292 of Mathematical Reviews Vol. , Issue 84d
[page]

1984
*
Mathematical Reviews
*

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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