On the density of certain languages with $p^2$ letters
| Autor: | Segovia, Carlos, Winklmeier, Monika |
|---|---|
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | The Electronic Journal of Combinatorics, Volume 22, Issue 3 (2015) |
| Druh dokumentu: | Working Paper |
| Popis: | The sequence $(x_n)_{n\in\mathbb N} = (2,5,15,51,187,\dots)$ given by the rule $x_n=(2^n+1)(2^{n-1}+1)/3$ appears in several seemingly unrelated areas of mathematics. For example, $x_n$ is the density of a language of words of length $n$ with four different letters. It is also the cardinality of the quotient of $(\mathbb Z_2\times \mathbb Z_2)^n$ under the left action of the special linear group $\mathrm{SL}(2,\mathbb Z)$. In this paper we show how these two interpretations of $x_n$ are related to each other. More generally, for prime numbers $p$ we show a correspondence between a quotient of $(\mathbb Z_p\times\mathbb Z_p)^n$ and a language with $p^2$ letters and words of length $n$. Comment: 10 pages, 2 figures. The section on cobordism categories was shortened. http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p16 |
| Databáze: | arXiv |
| Externí odkaz: |
|