The Maximal Order of Hyper-($b$-ary)-expansions

[摘要] Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant 2$.

[学科分类] 离散数学和组合数学

[关键词] Stern's diatomic sequence;Hyper base expansions;Maximal order