论文标题
将慢速解决方案连接到使用线性复发序列的嵌套复发
Connecting Slow Solutions to Nested Recurrences with Linear Recurrent Sequences
论文作者
论文摘要
标记的无限树提供了组合解释，用于嵌套复发关系产生的许多整数序列。通常，这样的序列是单调的增加。这些序列中的几个在序列中的每个值的频率上也具有直接的描述。在本文中，我们将最古典的示例推广到通过线性复发关系参数参数的较大序列。我们的每个序列都可以通过三种不同的方式构造：通过嵌套的复发关系，从标记的无限树或使用Zeckendorf样数字的字符串来描述其频率序列。我们通过讨论序列的渐近行为来结束论文。
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward descriptions in terms of how often each value in the sequence occurs. In this paper, we generalize the most classical examples to a larger family of sequences parametrized by linear recurrence relations. Each of our sequences can be constructed in three different ways: via a nested recurrence relation, from labeled infinite trees, or by using Zeckendorf-like strings of digits to describe its frequency sequence. We conclude the paper by discussing the asymptotic behaviors of our sequences.
