Simple permutations with order $4n + 2$. Part I

Simple permutations with order $4n + 2$ by means of Pasting and Reversing

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez \& Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behaviour of those periodic points. Recently Abdulla et al studied the structure of minimal $4n+2$-orbits of the continuous endomorphisms on the real line. This paper studies some combinatorial dynamics structures of permutations of mixed order $4n+2$, describing its genealogy, using P…

置换异或元胞自动机：部分移位连接与半本原多项式

Permutation XOR cellular automata: partial-shift connections and half-primitive polynomials

本文提出一种由异或规则与部分移位连接组成的置换异或元胞自动机，可生成长二进制周期轨道，并用半本原多项式表征，且实现了FPGA硬件。