In this article we introduce the readers to the concept of leading number", as proposed by D. Conway in the seventies of the last century. The leading number, associated to a word w, is a binary vector that describes some special aspects of the structure of w. We shall see that it conveys the essential information that is needed in the analysis of the time of occurrence of w in a random sequence of letters. The theme of time of occurrence of words, a sort of classical topic of applied probability, presents several aspects of interest. In particular, it gives rise to some apparently paradoxical conclusions. Furthermore it is related with the notion of fair games and leads to interesting mathematical problems.
Waiting for ABRACADABRA. Occurrence of Words and Leading Numbers / DE SANTIS, Emilio; Spizzichino, Fabio. - (2012), pp. 175-185. [10.1007/978-88-470-2427-4_17].
Waiting for ABRACADABRA. Occurrence of Words and Leading Numbers
DE SANTIS, Emilio;SPIZZICHINO, Fabio
2012
Abstract
In this article we introduce the readers to the concept of leading number", as proposed by D. Conway in the seventies of the last century. The leading number, associated to a word w, is a binary vector that describes some special aspects of the structure of w. We shall see that it conveys the essential information that is needed in the analysis of the time of occurrence of w in a random sequence of letters. The theme of time of occurrence of words, a sort of classical topic of applied probability, presents several aspects of interest. In particular, it gives rise to some apparently paradoxical conclusions. Furthermore it is related with the notion of fair games and leads to interesting mathematical problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
