论文标题
$ p $ - 序列的线性方案modulo $ p^r $
$p$-Linear schemes for sequences modulo $p^r$
论文作者
论文摘要
许多有趣的组合序列，例如Apéry数字和Franel数字，都享受所谓的Lucas Property Modulo几乎所有Primes $ P $。 Modulo Prime Powers $ p^r $这样的序列具有更复杂的行为，可以用Lucas属性的矩阵版本来描述，称为$ p $ - 线性方案。它们是有限$ p $ -automata的示例。在本文中，我们构建了这样的$ p $ - 线性方案，并为固定$ r $的状态数量提供上限，不依赖$ p $。
Many interesting combinatorial sequences, such as Apéry numbers and Franel numbers, enjoy the so-called Lucas property modulo almost all primes $p$. Modulo prime powers $p^r$ such sequences have a more complicated behaviour which can be described by matrix versions of the Lucas property called $p$-linear schemes. They are examples of finite $p$-automata. In this paper we construct such $p$-linear schemes and give upper bounds for the number of states which, for fixed $r$, do not depend on $p$.
