Arithmetic Properties of m-ary Partitions Without Gaps

被引：2
作者：
Andrews, George E. [1 ]
Brietzke, Eduardo [2 ]
Rodseth, Oystein J. [3 ]
Sellers, James A. [1 ]
机构：
[1] Penn State Univ, Dept Math, 104 McAllister Bldg, University Pk, PA 16802 USA
[2] Univ Fed Rio Grande do Sul, Inst Math, CP 15080, BR-91509900 Porto Alegre, RS, Brazil
[3] Univ Bergen, Dept Math, Allegt 41, N-5007 Bergen, Norway
来源：
ANNALS OF COMBINATORICS | 2017年 / 21卷 / 04期
关键词：
m-ary partitions; unique path partitions; congruences; CONGRUENCES;
D O I：
10.1007/s00026-017-0369-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Motivated by recent work of Bessenrodt, Olsson, and Sellers on unique path partitions, we consider partitions of an integer n wherein the parts are all powers of a fixed integer and there are no "gaps" in the parts; that is, if is the largest part in a given partition, then also appears as a part in the partition for each . Our ultimate goal is to prove an infinite family of congruences modulo powers of m which are satisfied by these functions.
引用
收藏
页码：495 / 506
页数：12
相关论文
共 24 条
  • [11] THREE DIFFERENT WAYS TO OBTAIN THE VALUES OF HYPER m-ARY PARTITION FUNCTIONS
    Eom, Jiae
    Jeong, Gyeonga
    Sohn, Jaebum
    [J]. Bulletin of the Korean Mathematical Society, 2016, 53 (06) : 1857 - 1868
  • [12] Arithmetic Properties of Certain t-Regular Partitions
    Rupam Barman
    Ajit Singh
    Gurinder Singh
    [J]. Annals of Combinatorics, 2024, 28 : 439 - 457
  • [13] Arithmetic Properties of Certain t-Regular Partitions
    Barman, Rupam
    Singh, Ajit
    Singh, Gurinder
    [J]. ANNALS OF COMBINATORICS, 2024, 28 (02) : 439 - 457
  • [14] Arithmetic properties for two restricted partitions modulo powers of 5
    Tang, Dazhao
    [J]. QUAESTIONES MATHEMATICAE, 2020, 43 (02) : 169 - 183
  • [15] Arithmetic properties of 5-regular partitions into distinct parts
    Baruah, Nayandeep Deka
    Sarma, Abhishek
    [J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2025, 21 (03) : 657 - 674
  • [16] Arithmetic Properties of Non-Squashing Partitions into Distinct Parts
    Øystein J. Rødseth
    James A. Sellers
    Kevin M. Courtright
    [J]. Annals of Combinatorics, 2004, 8 (3) : 347 - 353
  • [17] Arithmetic properties of 3-regular partitions with distinct odd parts
    V. S. Veena
    S. N. Fathima
    [J]. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2021, 91 : 69 - 80
  • [18] Arithmetic properties of 3-regular partitions with distinct odd parts
    Veena, V. S.
    Fathima, S. N.
    [J]. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2021, 91 (01): : 69 - 80
  • [19] Arithmetic Properties of 9-Regular Partitions with Distinct Odd Parts
    Hemanthkumar, B.
    Bharadwaj, H. S. Sumanth
    Naika, M. S. Mahadeva
    [J]. ACTA MATHEMATICA VIETNAMICA, 2019, 44 (03) : 797 - 811
  • [20] Arithmetic Properties of 9-Regular Partitions with Distinct Odd Parts
    B. Hemanthkumar
    H. S. Sumanth Bharadwaj
    M. S. Mahadeva Naika
    [J]. Acta Mathematica Vietnamica, 2019, 44 : 797 - 811
123