scholarly journals Shifted Distinct-part Partition Identities in Arithmetic Progressions

2017 ◽  
Vol 21 (4) ◽  
pp. 479-494
Author(s):  
Ethan Alwaise ◽  
Robert Dicks ◽  
Jason Friedman ◽  
Lianyan Gu ◽  
Zach Harner ◽  
...  
Keyword(s):  
Arithmetic Progressions ◽  
Partition Identities ◽  
Distinct Part

scholarly journals Proofs of some partition identities conjectured by Kanade and Russell

2021 ◽  
Author(s):  
Hjalmar Rosengren
Keyword(s):  
Lie Algebra ◽  
Partition Identities ◽  
Partition Identity ◽  
Affine Lie Algebra ◽  
Level 2

AbstractKanade and Russell conjectured several Rogers–Ramanujan-type partition identities, some of which are related to level 2 characters of the affine Lie algebra $$A_9^{(2)}$$ A 9 ( 2 ) . Many of these conjectures have been proved by Bringmann, Jennings-Shaffer and Mahlburg. We give new proofs of five conjectures first proved by those authors, as well as four others that have been open until now. Our proofs for the new cases use quadratic transformations for Askey–Wilson and Rogers polynomials. We also obtain some related results, including a partition identity conjectured by Capparelli and first proved by Andrews.

scholarly journals Colorings with only rainbow arithmetic progressions

2020 ◽  
Vol 161 (2) ◽  
pp. 507-515
Author(s):  
J. Pach ◽  
I. Tomon
Keyword(s):  
Arithmetic Progressions

scholarly journals New proof to Somos’s Dedekind eta-function identities of level 10

2021 ◽  
Author(s):  
B. R. Srivatsa Kumar ◽  
Shruthi
Keyword(s):  
Dedekind Eta Function ◽  
Partition Identities

AbstractMichael Somos used PARI/GP script to generate several Dedekind eta-function identities by using computer. In the present work, we prove two new Dedekind eta-function identities of level 10 discovered by Somos in two different methods. Also during this process, we give an alternate method to Somos’s Dedekind eta-function identities of level 10 proved by B. R. Srivatsa Kumar and D. Anu Radha. As an application of this, we establish colored partition identities.

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