Plane Partitions and Divisors-Reference-Cited by-同舟云学术

Plane Partitions and Divisors

Published:2023-12-19 Issue:1 Volume:16 Page:5
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Ballantine Cristina¹^ORCID,Merca Mircea²³^ORCID

Affiliation:

1. Department of Mathematics and Computer Science, College of The Holy Cross, Worcester, MA 01610, USA

2. Department of Mathematical Methods and Models, Fundamental Sciences Applied in Engineering Research Center, National University of Science and Technology Politehnica Bucharest, Bucharest 060042, Romania

3. Academy of Romanian Scientists, Bucharest 050044, Romania

Abstract

In this paper, we consider the sum of divisors d of n such that n/d is a power of 2 and derive a new decomposition for the number of plane partitions of n in terms of binomial coefficients as a sum over partitions of n. In this context, we introduce a new combinatorial interpretation of the number of plane partitions of n.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/16/1/5/pdf

Reference25 articles.

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3. Rogers-Rarnanujam identities for partitions with “N copies of N”;Agarwal;J. Combin. Theory Ser. A,1987

4. Bressoud, D.M. (1999). Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press.

5. Sloane, N.J.A. (2023, November 22). The On-Line Enciclopedia of Integer Sequences. Available online: http://oeis.org.