POWER PARTITIONS AND SEMI-m-FIBONACCI PARTITIONS

被引：1

作者：

Alanazi, Abdulaziz M. ^{[1
]}

Munagi, Augustine O. ^{[2
]}

Nyirenda, Darlison ^{[2
]}

机构：

[1] Univ Tabuk, Fac Sci, Dept Math, POB 741, Tabuk 71491, Saudi Arabia

[2] Univ Witwatersrand, Sch Math, PO Wits 2050, Johannesburg, South Africa

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2020年 / 102卷 / 03期

关键词：

partition; bijection; congruence;

D O I：

10.1017/S0004972720000027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Andrews ['Binary and semi-Fibonacci partitions', J. Ramanujan Soc. Math. Math. Sci. 7(1) (2019), 1-6] recently proved a new identity between the cardinalities of the set of semi-Fibonacci partitions and the set of partitions into powers of 2 with all parts appearing an odd number of times. We extend the identity to the set of semi-m-Fibonacci partitions of n and the set of partitions of n into powers of m in which all parts appear with multiplicity not divisible by m. We also give a new characterisation of semi-m-Fibonacci partitions and some congruences satisfied by the associated number sequence.

引用

页码：418 / 429

页数：12