关于非本原置换的Cobham定理

科巴姆代换定理

Cobham's theorem for substitutions

科巴姆的开创性定理在过去的40年里引起了许多关于非标准数制的工作，并已扩展到许多场合。在本文中，作为十五年的改进的结果，我们得到了一个完整的和一般的版本，所谓的替代序列。设$α$和$β$是两个乘法独立的Perron数。然后，序列$x\in A^\mathbb{N}$，其中$A$是有限字母表，当且仅当$x$最终是周期的时，是$α$ -替代的和$β$ -替代的。

Cobham定理的推广

A generalization of Cobham's Theorem

如果一个非周期序列$X$是一个本原代换$σ$和一个本原代换$τ$的不动点的态射的像，则$σ$和$τ$的矩阵的主特征值是乘法相关的。这就是我们提出的推广科巴姆定理的方法。

Cobham-Semenov定理与$\NN^d$ -子移位

Cobham-Semenov theorem and $\NN^d$-subshifts

我们给出了一个新的证明的Cobham的第一定理使用的想法从符号动力学和Cobham-Semenov定理（在原始的情况下）使用的想法从平铺动态。

Substitutive systems and a finitary version of Cobham's theorem

We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.

Anti-Powers in Primitive Uniform Substitutions

In a recent work, A. Berger and C. Defant showed that if $x$ is a fixed point of a binary uniform and primitive morphism, then there exists a constant $C$ such that for all positive integers $i,k,$ beginning in position $n$ in $x$ is a $k$-anti-power with block length at most $Ck$. They ask whether this result extends to a broader class of morphic words. In this note we extend their results to fixed points of uniform primitive morphisms on arbitrary finite alphabets. Our methods make use of the recognisability of uniform primitive morphisms. This result was proved independantly by S. Garg, usi…

Combinatorics of explicit substitutions

$λ\upsilon$ is an extension of the $λ$-calculus which internalises the calculus of substitutions. In the current paper, we investigate the combinatorial properties of $λ\upsilon$ focusing on the quantitative aspects of substitution resolution. We exhibit an unexpected correspondence between the counting sequence for $λ\upsilon$-terms and famous Catalan numbers. As a by-product, we establish effective sampling schemes for random $λ\upsilon$-terms. We show that typical $λ\upsilon$-terms represent, in a strong sense, non-strict computations in the classic $λ$-calculus. Moreover, typically almost …