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PROOFS OF CONJECTURES OF SANDON AND ZANELLO ON COLORED PARTITION IDENTITIES
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 Title & Authors
PROOFS OF CONJECTURES OF SANDON AND ZANELLO ON COLORED PARTITION IDENTITIES
Berndt, Bruce C.; Zhou, Roberta R.;
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 Abstract
In a recent systematic study, C. Sandon and F. Zanello offered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for multipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ramanujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan's catalogue of theta function formulas.
 Keywords
colored partitions;modular equations;theta function identities;
 Language
English
 Cited by
1.
Color Partition Identities Arising from Ramanujan’s Theta-Functions, Acta Mathematica Vietnamica, 2016  crossref(new windwow)
2.
Partition identities arising from Ramanujan’s formulas for multipliers, The Ramanujan Journal, 2015  crossref(new windwow)
3.
Identities for Partitions with Distinct Colors, Annals of Combinatorics, 2015, 19, 3, 397  crossref(new windwow)
4.
Some new identities for colored partition, The Ramanujan Journal, 2016, 40, 3, 473  crossref(new windwow)
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