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
Publication date:
19.3.2024.
Visits: 102 *