For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth left--to--right maximum, for fixed r and n !1. 1.

Stochastic complexity of a data set is defined as the shortest possible code length for the data obtainable by using some fixed set of models. This measure

Abstract. From recent work of Zhang and of Zagier, we know that their height H(α) is bounded away from 1 for every algebraic number α different from 0, 1, 1/2 ± √ −3/2. The study of the related spectrum is especially interesting, for it is linked to Lehmer’s problem and to a conjecture of Bogomolov. After recalling some definitions, we show an improvement of the so-called Zhang-Zagier inequality. To achieve this, we need some algebraic numbers of small height. So, in the third section, we describe an algorithm able to find them, and we give an algebraic number with height 1.2875274... discovered in this way. This search up to degree 64 suggests that the spectrum of H(α) mayhave a limit point less than 1.292. We prove this fact in the fourth part. 1.

A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; (3) the reduced automaton is used to compute an expression (in terms of stream constants and operators) that represents the stream of all counts.

Abstract not found

Coinductive counting: bisimulation in enumerative combinatorics (extended abstract)

and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of

CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.

We consider the task of computing the cycle structure of a permutation π on n numbers. The permutation is given as an oracle, that is, when we specify x, we get back π(x) from the oracle, but have no further knowledge about the permutation’s structure. By computing the cycle structure of π, we mean that a list is generated that

Abstract not found