We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon’s combinatorial generalization of the Rogers-Ramanujan identities. The implications of applying the same map to a special case of David Bressoud’s even modulus analog of Gordon’s theorem are also explored.

Copyright: © 2017 Rogers IM, This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. *Corresponding author: Rogers IM, Anesthesiology, 46 Whitburn Road, Cleadon, Tyne and Wear SR67QS, Sunderland, UK, Tel: 01915367944; ...

1.1 q -binomial coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 1.2 Unimodality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 1.3 Congruences for the partition function . . . . . . . . . . . . . . . . . . . . . . . . . 143 1.4 The Jacobi triple product identity . . . . . . . . . . . . . . . . . ...

Garrett, Ismail, and Stanton gave a general formula that contains the Rogers{ Ramanujan identities as special cases. The theory of associated orthogonal polynomials is then used to explain determinants that Schur introduced in 1917 and show that the Rogers{Ramanujan identities imply the Garrett, Ismail, and Stanton seemingly more general formula. Using a result of Slater a continued fraction is...

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

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. AMS Subject Classification. 05A19; secondary 11B65, 05A17

New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.