Identityfinder and some new identities of Rogers-Ramanujan type.(English)Zbl 1327.11075
Two of the most important results in the theory of \(q\)-series are the classical Rogers-Ramanujan identities. The two Rogers-Ramanujan identities and various analogous identities (Euler, Gordon, Andrews-Bressoud, Capparelli, etc.), which equate certain infinite products with infinite sums, are among the most intriguing of the classical formal power series identities. The authors used the Maple package {IdentityFinder}, a systematic mechanism based on symbolic computation, to derive six new conjectured identities of Rogers-Ramanujan type.
Reviewer: Mircea Merca (Cornu)
MSC:
| 11P84 | Partition identities; identities of Rogers-Ramanujan type |
| 05A15 | Exact enumeration problems, generating functions |
| 05A17 | Combinatorial aspects of partitions of integers |
| 17B69 | Vertex operators; vertex operator algebras and related structures |
Cite
Online Encyclopedia of Integer Sequences:
Number of partitions of n into parts congruent to 1, 3, 6, 8 (mod 9).References:
| [1] | Andrews [Andrews 76] G. E., The Theory of Partitions (1998) |
| [2] | E [Andrews 78] G., Groupe d’Etude d’Algebre 8 (1978) |
| [3] | E [Andrews 92] G., Proc. Rademacher Centenary Conf., 1992, Contemp. Math. 166 pp 141– (1994) |
| [4] | DOI: 10.2307/2325145 ·Zbl 0681.10009 ·doi:10.2307/2325145 |
| [5] | DOI: 10.1023/A:1009719322309 ·Zbl 0905.11044 ·doi:10.1023/A:1009719322309 |
| [6] | DOI: 10.1007/BF01011427 ·Zbl 0511.05004 ·doi:10.1007/BF01011427 |
| [7] | DOI: 10.1016/j.jcta.2007.02.004 ·Zbl 1126.11056 ·doi:10.1016/j.jcta.2007.02.004 |
| [8] | DOI: 10.1007/BF01940329 ·Zbl 0388.17006 ·doi:10.1007/BF01940329 |
| [9] | DOI: 10.1073/pnas.78.12.7254 ·Zbl 0472.17005 ·doi:10.1073/pnas.78.12.7254 |
| [10] | DOI: 10.1007/BF01388447 ·Zbl 0577.17009 ·doi:10.1007/BF01388447 |
| [11] | DOI: 10.1007/BF01388515 ·Zbl 0577.17010 ·doi:10.1007/BF01388515 |
| [12] | DOI: 10.1007/s11139-012-9388-4 ·Zbl 1256.05014 ·doi:10.1007/s11139-012-9388-4 |
| [13] | DOI: 10.1016/j.jsc.2009.02.003 ·Zbl 1175.33018 ·doi:10.1016/j.jsc.2009.02.003 |
| [14] | DOI: 10.1016/0001-8708(87)90008-9 ·Zbl 0635.17006 ·doi:10.1016/0001-8708(87)90008-9 |
| [15] | Meurman [Meurman and Primc 99] A., Mem. Am. Math. Soc. 137 pp 652– (1999) |
| [16] | DOI: 10.1142/S0219199701000512 ·Zbl 1004.17003 ·doi:10.1142/S0219199701000512 |
| [17] | Sills [Sills 03] A., Electronic J. Combin. 10 (1) pp 122– (2003) |
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