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Properties of Multivariate $${\varvec{b}}$$b -Ary Stern Polynomials
Annals of Combinatorics ( IF 0.6 ) Pub Date : 2019-11-15 , DOI: 10.1007/s00026-019-00464-5
Karl Dilcher , Larry Ericksen

Given an integer base \(b\ge 2\), we investigate a multivariate b-ary polynomial analogue of Stern’s diatomic sequence which arose in the study of hyper b-ary representations of integers. We derive various properties of these polynomials, including a generating function and identities that lead to factorizations of the polynomials. We use some of these results to extend an identity of Courtright and Sellers on the b-ary Stern numbers \(s_b(n)\). We also extend a result of Defant and a result of Coons and Spiegelhofer on the maximal values of \(s_b(n)\) within certain intervals.

中文翻译:

多元$$ {\ varvec {b}} $$ b -Ary Stern多项式的性质

给定一个整数基\(b \ ge 2 \),我们研究了斯特恩双原子序列的多元b元多项式类似物,它是在研究整数的超b元表示形式时出现的。我们导出这些多项式的各种属性,包括生成函数和导致多项式分解的恒等式。我们使用了一些这些结果对延长Courtright和卖家的身份b进制数字斯特恩\(S_B(N)\) 。我们还扩展了Defant的结果以及Coons和Spiegelhofer的结果在一定间隔内对\(s_b(n)\)的最大值的影响。
更新日期:2019-11-15
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