Original scientific paper

A note on the number of plane partitions and r-component multipartitions of n

Mircea Cimpoeas orcid.org/0000-0002-7774-9883 ; aculty of Applied Sciences, University Politehnica of Bucharest, Corp BN, Bucharest , Romania *
Alexandra Teodor

* Corresponding author.

Abstract

Using elementary methods, we prove new formulas for \(\pp(n)\), the number of plane partitions of \(n\), \(\pp_r(n)\), the number
of plane partitions of \(n\) with at most \(r\) rows, $\pps(n)$, the number of strict plane partitions of \(n\)
and \(\ppso(n)\), the number of symmetric plane partitions of \(n\). Also, we give new formulas for \(P_r(n)\),
the number of \(r\)-component multipartitions of \(n\).

Keywords

Integer partition, Restricted partition function, Plane partition, Multipartition

Hrčak ID:

315322

URI

https://hrcak.srce.hr/315322

Publication date:

19.3.2024.

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