Parity results for broken 5-diamond, 7-diamond and 11-diamond partitions

DOI10.1142/S179304211550027XzbMath1318.11133OpenAlexW2010032561MaRDI QIDQ5248138

Nayandeep Deka Baruah, Zakir Hussain Ahmed

Publication date: 27 April 2015

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s179304211550027x

zbMATH Keywords

theta functioncongruencebroken \(k\)-diamond partitiondissection

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)

Related Items (9)

Infinite families of congruences modulo 7 for broken 3-diamond partitions ⋮ New congruences for \(t\)-core partitions and Andrews' singular overpartitions ⋮ Congruences modulo 4 for broken \(k\)-diamond partitions ⋮ Note on the parity of broken 11-diamond partitions ⋮ Extensive parity analysis of broken 5-diamond partitions ⋮ Parity results for broken 11-diamond partitions ⋮ CONGRUENCES MODULO 2 FOR CERTAIN PARTITION FUNCTIONS ⋮ A note on the parity of broken 7-diamond partitions ⋮ More parity results for broken 9-diamond partitions

Cites Work

• Congruences for broken \(k\)-diamond partitions
• Arithmetic properties of \(\ell\)-regular partitions
• New parity results for broken 11-diamond partitions
• Infinite families of strange partition congruences for broken 2-diamonds
• Analogues of Ramanujan's partition identities and congruences arising from his theta functions and modular equations
• Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions
• An extensive analysis of the parity of broken 3-diamond partitions
• Some congruences for Andrews-Paule's broken 2-diamond partitions
• Elementary proofs of parity results for broken 3-diamond partitions
• Parity results for broken k-diamond partitions and (2k+1)-cores
• COMBINATORIAL PROOF OF ONE CONGRUENCE FOR THE BROKEN 1-DIAMOND PARTITION AND A GENERALIZATION
• MacMahon's partition analysis XI: Broken diamonds and modular forms
• On recent congruence results of Andrews and Paule for broken k-diamonds
• ON THE BROKEN 1-DIAMOND PARTITION
• Cubic Analogues of the Jacobian Theta Function θ(z, q)
• MacMahon's partition analysis. VIII: Plane partition diamonds

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