A multi-dimensional extension of Sylvester’s identity-Reference-Cited by-同舟云学术

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A multi-dimensional extension of Sylvester’s identity

Published:2017-10-16 Issue:10 Volume:13 Page:2487-2504
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Alladi Krishnaswami¹

Affiliation:

1. Department of Mathematics, University of Florida, Gainesville, FL 32611, USA

Abstract

We obtain by combinatorial means, a multi-dimensional extension of Sylvester’s famous identity of 1882 that generalized Euler’s Pentagonal Numbers Theorem. We also provide a purely [Formula: see text]-hypergeometric proof.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304211750138X

Reference9 articles.

1. A combinatorial correspondence related to Göllnitz’ (big) partition theorem and applications

2. Generalizations of Schur's partition theorem

3. A new generalization of Schur's second partition theorem

4. A General Theorem on Partitions with Difference Conditions

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1. Combinatorial proofs and refinements of three partition theorems of Andrews;The Ramanujan Journal;2022-08-07

2. Overconvergent Eichler-Shimura isomorphisms for unitary Shimura curves over totally real fields;Israel Journal of Mathematics;2021-04

3. Multi-dimensional q-summations and multi-colored partitions;The Ramanujan Journal;2019-01-17

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