Some Rogers-Ramanujan type partition theorems
نویسندگان
چکیده
منابع مشابه
Some Partition Theorems of the Rogers-Ramanujan Type
Some partition theorems similar to the Rogers-Ramanujan theorems are proved. We shall prove the following partition theorems, namely THEOREM 1. The number of partitions of k, k = a 1 + a 2 + a 3 + · · · with a 1 > a 2 ≥ a 3 > a 4 ≥ · · ·
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This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi’s celebrated triple product identity for theta functions, Sylvester’s famous refinement of Euler’s theorem, as we...
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Abstract. By using the KMN2 crystal base character formula for the basic A (1) 2 module, and the principally specialized Weyl-Kac character formula, we obtain a Rogers-Ramanujan type combinatorial identity for colored partitions. The difference conditions between parts are given by the energy function of certain perfect A (1) 2 crystal. We also recall some other identities for this type of colo...
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In this we paper we prove several new identities of the RogersRamanujan-Slater type. These identities were found as the result of computer searches. The proofs involve a variety of techniques, including constant-term methods, Bailey pairs, a theorem of Watson on basic hypergeometric series and the method of q-difference equations.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1985
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1985.120.431