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SOME INEQUALITIES ON RANKS OF CUBIC PARTITIONS
被引:0
作者:
Fan, Yan
[1
]
Xia, Ernest X. W.
[2
]
机构:
[1] Jiangsu Univ, Dept Math, Zhenjiang, Peoples R China
[2] Suzhou Univ Sci & Technol, Sch Math Sci, Suzhou, Peoples R China
基金:
中国国家自然科学基金;
关键词:
cubic partitions;
rank;
inequalities;
q-series technique;
CONTINUED-FRACTION;
MODULO POWERS;
CRANK;
CONGRUENCES;
NUMBER;
ANALOG;
D O I:
10.1216/rmj.2024.54.1315
中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
A partition is a cubic partition if its even parts come in two colors (blue and red). Reti defined the rank of a cubic partition as the difference between the number of even parts in blue color and the number of even parts in red color. Motivated by the works on inequalities of rank and crank for certain partitions proved by Andrews and Lewis, and Chern, Fu, Tang and Wang, we prove some inequalities for N '(r, m, n), which count the number of cubic partitions of n whose rank is congruent to r modulo m. More precisely, we establish the generating functions for N '(r, m, n) and determine the signs of the differences N '(r, m ,n)-N '(s, m, n)with m is an element of{2, 3, 4, 6} and 0 <= r< s <= m -1 by utilizing q-series techniques in this paper.
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页码:1315 / 1329
页数:15
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