A palindromization map for the free group

The palindromization map

The palindromization map has been defined initially by Aldo de Luca in the context of Sturmian words. It was extended to the free group of rank $2$ by Kassel and the second autho We extend their construction to arbitrary alphabets. We also investigate the suffix automaton and compact suffix automaton of the words obtained by palindromization.

A generalized palindromization map in free monoids

The palindromization map $ψ$ in a free monoid $A^*$ was introduced in 1997 by the first author in the case of a binary alphabet $A$, and later extended by other authors to arbitrary alphabets. Acting on infinite words, $ψ$ generates the class of standard episturmian words, including standard Arnoux-Rauzy words. In this paper we generalize the palindromization map, starting with a given code $X$ over $A$. The new map $ψ_X$ maps $X^*$ to the set $PAL$ of palindromes of $A^*$. In this way some properties of $ψ$ are lost and some are saved in a weak form. When $X$ has a finite deciphering delay on…

有限群与具有平方自由欧拉特征的弧传递映射

Finite groups and arc-transitive maps of square-free Euler characteristic

本文研究了有限群在具有平方自由欧拉特征的映射上弧传递作用的特征化，并关联了无限族的正则映射。

Envy-free division using mapping degree

In this paper we study envy-free division problems. The classical approach to such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions for this map to hit the center of the simplex. The mere continuity of the map is not sufficient for reaching such a conclusion. Classically, one makes additional assumptions on the behavior of the map on the boundary of the simplex (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem). We follow Erel Segal-Halevi, Frédéric Meunier, and Shira Zerbib, and replace the …