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Showing 1 to 2 of 2 for “"colored partitions"”.
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Bijective proofs of partition identities and covering systems
… two topics. The first is on the theory of partitions, which is discussed in Chapters 2 − 5. The second is on covering systems, which are considered in Chapters 6 − 8. In 2000, Farkas and Kra used their theory of theta functions to establish a beautiful theorem on colored partitions, and …
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Modular equations and Ramanujan's cubic and quartic theories of theta functions
"In this thesis, we prove several identities involving Ramanujan's general theta function. In Chapter 2, we give proofs for new Ramanujan type modular equations discovered by Somos and establish applications of some of them. In Chapter 3, we will give proofs for several Dedekind eta product …