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Some More Identities Of Rogers-Ramanujan Type, Douglas Bowman, James Mclaughlin, Andrew Sills
Some More Identities Of Rogers-Ramanujan Type, Douglas Bowman, James Mclaughlin, Andrew Sills
Department of Mathematical Sciences Faculty Publications
In this we paper we prove several new identities of the Rogers-Ramanujan-Slater type. These identities were found as the result of computer searches. The proofs involve a variety of techniques, including series-series identities, Bailey pairs, a theorem of Watson on basic hypergeometric series, generating functions and miscellaneous methods.
A Partition Bijection Related To The Rogers-Selberg Identities And Gordon's Theorem, Andrew Sills
A Partition Bijection Related To The Rogers-Selberg Identities And Gordon's Theorem, Andrew Sills
Department of Mathematical Sciences Faculty Publications
We provide a bijective map from the partitions enumerated by the series side of the Rogers–Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers–Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored.
On The Simplification Of Certain Q-Multisums, Andrew Sills
On The Simplification Of Certain Q-Multisums, Andrew Sills
Department of Mathematical Sciences Faculty Publications
Some examples of naturally arising multisum q-series which turn out to have representations as fermionic single sums are presented. The resulting identities are proved using transformation formulas from the theory of basic hypergeometric series.