原像大小受限的函数迭代周期
组合数学
2018-10-10 v3
摘要
我们考虑在 n = kr 个节点上的随机映射，其原像大小限制为形如 {0,k} 的集合，其中 k = k(r) 大于 1。我们证明 T（循环长度的最小公倍数）与 B（循环长度的乘积）均渐近对数正态。这些随机变量的期望值也被估计并与数值结果比较。该工作部分受这些映射被用作形如 x^k + a 的多项式在模 p 整数（其中 p 同余于 1 mod k）上的启发式模型所推动。
引用
@article{arxiv.1701.09148,
title = {Periods of iterations of functions with restricted preimage sizes},
author = {Rodrigo S. V. Martins and Daniel Panario and Claudio Qureshi and Eric Schmutz},
journal= {arXiv preprint arXiv:1701.09148},
year = {2018}
}
备注
An extended abstract of this work was presented at the 29th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Some corrections and improvevments have been made