Geodesic
Further Theorems of the Rogers-Ramanujan Type Theorems*
Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 210-214

Voir la notice de l'article provenant de la source Cambridge University Press

We give three new partition theorems of the classical Rogers-Ramanujan type which are very much in the style of MacMahon. These are a continuation of four theorems of the same kind given recently by the second author. One of these new theorems, very similar to one of the original Rogers-Ramanuj an - MacMahon type theorems is as follows: Let C(n) denote the number of partitions of n into parts congruent to ±2, ± 3,±4,± 5,±6,±7 (mod 20). Let D(n) denote the number of partitions of n of the form n = b1 + b2 + ... + bt, where bt ≧ 2, bt ≧ bi + 1 and if 1 ≦ i ≦ [(t - 2)/2], bi - bi + 1 ≧ 2. Then C(n) = D(n).
DOI : 10.4153/CMB-1988-032-3
Mots-clés : Partitions, congruences, generating functions, 10A45 
Subbarao, M. V.; Agarwal, A. K. Further Theorems of the Rogers-Ramanujan Type Theorems*. Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 210-214. doi: 10.4153/CMB-1988-032-3
@article{10_4153_CMB_1988_032_3,
     author = {Subbarao, M. V. and Agarwal, A. K.},
     title = {Further {Theorems} of the {Rogers-Ramanujan} {Type} {Theorems*}},
     journal = {Canadian mathematical bulletin},
     pages = {210--214},
     year = {1988},
     volume = {31},
     number = {2},
     doi = {10.4153/CMB-1988-032-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-032-3/}
}
TY  - JOUR
AU  - Subbarao, M. V.
AU  - Agarwal, A. K.
TI  - Further Theorems of the Rogers-Ramanujan Type Theorems*
JO  - Canadian mathematical bulletin
PY  - 1988
SP  - 210
EP  - 214
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-032-3/
DO  - 10.4153/CMB-1988-032-3
ID  - 10_4153_CMB_1988_032_3
ER  - 
%0 Journal Article
%A Subbarao, M. V.
%A Agarwal, A. K.
%T Further Theorems of the Rogers-Ramanujan Type Theorems*
%J Canadian mathematical bulletin
%D 1988
%P 210-214
%V 31
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-032-3/
%R 10.4153/CMB-1988-032-3
%F 10_4153_CMB_1988_032_3

[1] 1. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers, Oxford University Press (5th Edition), 1983. Google Scholar

[2] 2. Hirschhorn, M. D., Some partition theorems of the Rogers-Ramanujan type, J. Combinatorial Theory, Series A, Vol. 27, No. 1 (1979), pp. 33–37. Google Scholar

[3] 3. Subbarao, M. V., Some Rogers-Ramanuj an type partition theorems, Pacific J. Math., Vol. 120 (1985), pp. 431–435. Google Scholar

[4] 4. Slater, L. J., Further identities of the Rogers-Ramanuj an type, Proc. London Math. Soc, Vol. 54 (1951-52), pp. 147–167. Google Scholar

Cité par Sources :