New combinatorial interpretations of two analytic identities
Author:
A. K. Agarwal
Journal:
Proc. Amer. Math. Soc. 107 (1989), 561-567
MSC:
Primary 05A19; Secondary 05A15, 05A17, 11P57
DOI:
https://doi.org/10.1090/S0002-9939-1989-0979216-7
MathSciNet review:
979216
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Two generalized partition theorems involving partitions with "
copies of 
" and " 
copies of 
", respectively, are proved. These theorems have potential of yielding infinite Rogers-Ramanujan type identities on MacMahon's lines. Five particular cases are also discussed. Among them three are known and two provide new combinatorial interpretations of two known 
-identities.
- [1] A. K. Agarwal, Partitions with “𝑁 copies of 𝑁”, Combinatoire énumérative (Montreal, Que., 1985/Quebec, Que., 1985) Lecture Notes in Math., vol. 1234, Springer, Berlin, 1986, pp. 1–4. MR 927753, https://doi.org/10.1007/BFb0072504
- [2] A. K. Agarwal, Rogers-Ramanujan identities for 𝑛-color partitions, J. Number Theory 28 (1988), no. 3, 299–305. MR 932378, https://doi.org/10.1016/0022-314X(88)90045-5
- [3] A. K. Agarwal and George E. Andrews, Rogers-Ramanujan identities for partitions with “𝑛 copies of 𝑛”, J. Combin. Theory Ser. A 45 (1987), no. 1, 40–49. MR 883892, https://doi.org/10.1016/0097-3165(87)90045-8
- [4] A. K. Agarwal and David M. Bressoud, Lattice paths and multiple basic hypergeometric series, Pacific J. Math. 136 (1989), no. 2, 209–228. MR 978611
- [5] W. N. Bailey, On the simplification of some identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (3) 1 (1951), 217–221. MR 0043839, https://doi.org/10.1112/plms/s3-1.1.217
- [6] L. J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952), 147–167. MR 49225, https://doi.org/10.1112/plms/s2-54.2.147
copies of 
", Lecture Notes in Math., no. 1234, Proceedings of the Colloque de Combinatorie Énumerative, University of Quebec at Montreal, Springer-Verlag, 1985, pp. 1-4. 
-color partitions, J. Number Theory 28 (1988), 299-305. 
copies of 
," J. Combin. Theory Ser. A, 45, No. 1 (1987), 40-49. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05A19, 05A15, 05A17, 11P57
Retrieve articles in all journals with MSC: 05A19, 05A15, 05A17, 11P57
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1989-0979216-7
Keywords:
Partitions,
weighted differences,
-identities,
combinatorial interpretations
Article copyright:
© Copyright 1989
American Mathematical Society
