Plane Partitions as Sums over Partitions

被引：3
|
作者：
Merca, Mircea [1 ,2 ]
Radu, Iulia-Ionelia [3 ]
机构：
[1] Univ Politehn Bucuresti, Fundamental Sci Appl Engn Res Ctr, Dept Math Methods & Models, Bucharest 060042, Romania
[2] Acad Romanian Scientists, Bucharest 050044, Romania
[3] Aurel Vlaicu High Sch, Breaza 105400, Romania
来源：
SYMMETRY-BASEL | 2023年 / 15卷 / 10期
关键词：
partitions; plane partitions; symmetric functions; binomial coefficients;
D O I：
10.3390/sym15101820
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we consider complete homogeneous symmetric functions and provide a new formula for the number of plane partitions of n. This formula expresses the number of plane partitions of n in terms of binomial coefficients as a sum over all the partitions of n, considering the multiplicity of the parts greater than one. We obtain similar results for the number of strict plane partition of n and the number of symmetric plane partitions of n.
引用
收藏
页数：14
相关论文
共 50 条
  • [1] OVERPARTITIONS AS SUMS OVER PARTITIONS
    Merca, Mircea
    PROCEEDINGS OF THE ROMANIAN ACADEMY SERIES A-MATHEMATICS PHYSICS TECHNICAL SCIENCES INFORMATION SCIENCE, 2021, 22 (04): : 325 - 331
  • [2] n-Color Partitions into Distinct Parts as Sums over Partitions
    Merca, Mircea
    Simion, Emil
    SYMMETRY-BASEL, 2023, 15 (11):
  • [3] The powers of two as sums over partitions
    Merca, Mircea
    QUAESTIONES MATHEMATICAE, 2021, 44 (12) : 1745 - 1755
  • [4] RECIPROCAL SUMS OVER PARTITIONS AND COMPOSITIONS
    KNOPFMACHER, A
    RIDLEY, JN
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 1993, 6 (03) : 388 - 399
  • [5] The reciprocal of (q; q)n as sums over partitions
    Merca, Mircea
    RAMANUJAN JOURNAL, 2021, 56 (03): : 1089 - 1097
  • [6] RAMANUJAN’S TAU FUNCTION AS SUMS OVER PARTITIONS
    Goran-Dumitru, Andreea
    Merca, Mircea
    UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2024, 86 (03): : 69 - 80
  • [7] RAMANUJAN'S TAU FUNCTION AS SUMS OVER PARTITIONS
    Goran-Dumitru, Andreea
    Merca, Mircea
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2024, 86 (03): : 69 - 80
  • [8] Padovan numbers as sums over partitions into odd parts
    Ballantine, Cristina
    Merca, Mircea
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, : 1 - 14
  • [9] Padovan numbers as sums over partitions into odd parts
    Cristina Ballantine
    Mircea Merca
    Journal of Inequalities and Applications, 2016
  • [10] Dominance Method for Plane Partitions Ⅲ—Flagged Skew Plane Partitions
    初文昌
    Acta Mathematica Sinica,English Series, 1989, (04) : 321 - 328
12345