常递归序列幂的复杂度
Complexity of powers of a constant-recursive sequence
AI总结：
本文研究常递归序列幂的秩序列，并在特征多项式有重根时回答了 Stinchcombe 关于其复杂度的问题。
摘要：
常递归序列是满足线性递推关系的序列，即后续项可由前面若干项的线性组合得到。常递归序列的秩是满足此类递推所需的最少前项数。对于常递归序列 $s(n)$，我们研究序列 $\left(\text{rank}\\, s(n)^M\right)_{M\geq 1}$。当特征多项式的根并非全部互异时，我们回答了 Stinchcombe 关于常递归序列幂的复杂度的问题。
英文摘要：
Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms required for such a recurrence. For a constant-recursive sequence $s(n)$, we study the sequence $\left(\text{rank}\, s(n)^M\right)_{M\geq 1}$. We answer a question of Stinchcombe regarding the complexity of the powers of a constant-recursive sequence when the roots of the characteristic polynomial are not all distinct.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
