Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(5): 1279-1287

Online first article June 29, 2022      Printed September 30, 2022

https://doi.org/10.4134/BKMS.b210749

Copyright © The Korean Mathematical Society.

Enumeration of relaxed complete partitions and double-complete partitions

Suhyung An, Hyunsoo Cho

Yonsei University; Ewha Womans University

Abstract

A partition of $n$ is complete if every positive integer from $1$ to $n$ can be represented by the sum of its parts. The concept of complete partitions has been extended in several ways. In this paper, we consider the number of $k$-relaxed $r$-complete partitions of $n$ and the number of double-complete partitions of $n$.

Keywords: Complete partitions, relaxed complete partitions, double-complete partitions

MSC numbers: Primary 05A17; Secondary 11P81

Supported by: Suhyung An was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (No. 2019R1I1A1A01059433). Hyunsoo Cho was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2021R1C1C2007589) and the Ministry of Education (No. 2019R1A6A1A11051177).

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