An Easy Proof of the Rogers - Ramanujan Identities
نویسنده
چکیده
Here and throughout this paper 191 is strictly less than one. Two new proofs of these identities have recently been announced. The first, by Lepowsky and Wilson [7], uses a Lie algebraic interpretation of the identities. The second, by Garsia and Milne (41, relies on the combinatorial interpretation and establishes the correspondence between the partitions which are counted by each side. Both of these proofs are enlightening but difficult. What is being presented here is the one type of proof Hardy and Wright despaired of ever finding when they wrote [6, p. 2921: “No proof is really easy (and it would perhaps be unreasonable to expect an easy proof).” The Rogers-Ramanujan identities bear at least superficial resemblance to the triple product identity of Jacobi:
منابع مشابه
Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type
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
متن کاملEasy Computer Proofs of the Rogers - RamanujanIdentities and of Identities of Similar
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.
متن کاملProofs of the Rogers - RamanujanIdentities and of Identities of Similar
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.
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where a = 0 or 1, are among the most famous q-series identities in partitions and combinatorics. Since their discovery the Rogers-Ramanujan identities have been proved and generalized in various ways (see [2, 4, 5, 13] and the references cited there). In [13], by adapting a method of Macdonald for calculating partial fraction expansions of symmetric formal power series, Stembridge gave an unusu...
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