Proofs of two conjectures on truncated series

DOI10.1016/J.JCTA.2014.10.004zbMath1316.11092OpenAlexW2017191343WikidataQ113871634 ScholiaQ113871634MaRDI QIDQ476284

Renrong Mao

Publication date: 28 November 2014

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2014.10.004

zbMATH Keywords

partitionsJacobi's identityJacobi's triple product identity

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81)

Related Items (27)

Lambert series and conjugacy classes in \(\mathrm{GL}\) ⋮ Infinite families of Hecke-Rogers type series and their truncated representations ⋮ Truncated versions of three identities of Euler and Gauss ⋮ Linear inequalities concerning partitions into distinct parts ⋮ Truncated sums for Hecke-Rogers type identities and Andrews-Hickerson's Bailey pair ⋮ Binomial transforms and integer partitions into parts of \(k\) different magnitudes ⋮ Combinatorial proofs of two truncated theta series theorems ⋮ Truncated theta series and a problem of Guo and Zeng ⋮ On Two Truncated Quintuple Series Theorems ⋮ A generalized truncated sums of Jacobi triple product series and some related truncated theorems ⋮ Truncated sums for certain restricted partition functions and transformation formulas for basic hypergeometric series ⋮ Truncated Hecke-Rogers type series. II ⋮ Rank partition functions and truncated theta identities ⋮ A note on the partitions involving parts of \(k\) different magnitudes ⋮ Unnamed Item ⋮ A truncated Jacobi triple product theorem ⋮ Bilateral truncated Jacobi's identity ⋮ Truncated Theta Series and Rogers-Ramanujan Functions ⋮ Note on the truncated generalizations of Gauss's square exponent theorem ⋮ Truncated Jacobi triple product series ⋮ Some new expansions for certain truncated \(q\)-series ⋮ Truncated series from the quintuple product identity ⋮ A truncated theta identity of Gauss and overpartitions into odd parts ⋮ Truncated Hecke-Rogers type series ⋮ New truncated theorems for three classical theta function identities ⋮ A Bailey type identity with applications related to integer representations ⋮ Truncations of Gauss' square exponent theorem

Cites Work

• Unnamed Item
• The truncated pentagonal number theorem
• A truncated Jacobi triple product theorem
• Interpreting the truncated pentagonal number theorem using partition pairs
• Rank and conjugation for a second Frobenius representation of an overpartition
• \(M_2\)-rank differences for partitions without repeated odd parts
• Some observations on Dyson's new symmetries of partitions
• Fast algorithm for generating ascending compositions
• Two truncated identities of Gauss
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Partial Theta Functions. I. Beyond the Lost Notebook

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