On congruences for q-analogues of ballot numbers

被引：0
|
作者：
Koparal, Sibel [1 ]
机构：
[1] Kocaeli Univ, Dept Math, Fac Sci & Arts, Kocaeli, Turkey
来源：
TURKISH JOURNAL OF MATHEMATICS | 2019年 / 43卷 / 05期
关键词：
Congruence; q-binomial coefficient; cyclotomic polynomial; ballot number;
D O I：
10.3906/mat-1905-88
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we examine some congruences with q-analogues of ballot numbers. For example, for n > 1 and d = 0, 1, ..., n - 1, Sigma(n-d)(k=1) q(k) B-k,d(q) (math) -2 + (-1)(n-d) (n - d +1/3) q(-1/3(n-d/2)) - (n - d - 1/3) q(d+1-1/3(n-d-2/2)) (mod Phi(n)(q)), with the Legendre symbol (./3), the q-analogue of ballot number B-n,d(q) and the nth cyclotomic polynomial Phi(n) (q).
引用
收藏
页码：2642 / 2648
页数：7
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