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Partition Identities for Ramanujan's Third Order Mock Theta Functions
mock theta function Ramanujan's identities partition identity Fine's theorem involution
2014/6/3
We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions φ(-q) and ψ(-q). We also give an involution for Fine's partition identity on th...
Euler's Partition Theorem with Upper Bounds on Multiplicities
partition Euler's partition theorem Sylvester's bijection
2014/6/3
We show that the number of partitions of n with alternating sum k such that the multiplicity of each part is bounded by 2m + 1 equals the number of partitions of n with k odd parts such that the multi...
A Unification of Two Refinements of Euler's Partition Theorem
partition Euler's partition theorem refinement bijection Bessenrodt's bijection Andrews-Olsson's theorem
2014/6/3
We obtain a unification of two refinements of Euler's partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt's insertion algorithm for a generalization of the An...
On Stanley's Partition Function
partition function Jacobi's triple product identity hook length
2014/6/3
Stanley defined a partition function t(n) as the number of partitions λ of n such that the number of odd parts of λ is congruent to the number of odd parts of the conjugate partition λ' modulo 4. We s...