Related papers: An Episode in The Old Mathematical Intelligencer
The Countdown game is one of the oldest TV show running in the world. It started broadcasting in 1972 on the french television and in 1982 on British channel 4, and it has been running since in both countries. The game, while extremely…
An exposition of the 1918 paper of Latt\`es, together with its historical antecedents, and its modern formulations and applications.
One of the most exciting results of the Spitzer era has been the ability to construct longitudinal brightness maps from the infrared phase variations of hot Jupiters. We presented the first such map in Knutson et al. (2007), described the…
The classical Gauss Map is a piecewise continuous map from the unit interval to itself. From this map we retrieve the continued fraction expansion of irrational numbers and its dynamical properties give information about some arithmetic and…
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…
This is a short account of connections between the Tutte polynomial and the Ising, Potts, and random-cluster models. The four principal elements are the Ising model of 1925, the Tutte polynomial of 1947, the Potts model of 1952, and the…
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.
We review the history of the automation of mathematical induction
"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers…
We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.
This is a quick survey on some recent works done in the field of random maps.
This article (which appeared with illustrations) was the astrophysics/cosmology contribution to the historical series ``Pathways of Discovery'' which appeared in ``Science'' during last year.
This is a preliminary investigation of the geometry and dynamics of rational maps with only two critical points. (originally titled ``On Bicritical Rational Maps'' in September 1997; revised and retitled April 1999)
An expository introduction to bidding chess and other bidding games. To appear in Mathematical Intelligencer.
This preprint appeared firstly in Russian in 1997. Some truncated versions of this preprint were published in English and French, here a fully translated version is presented. The translation in English was done by O. V. Feodoritova and V.…
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give…
This paper deals with the history of Density-Wave Spiral Theories in the 1960s. The motivation to write the paper was the publication of two papers on the history of these theories (Pasha 2004a,b). Pasha's papers tell only a part of the…
In 1970, Statistics giant, Bradley Efron, amazed the world by coming up with a set of four dice, let's call them A,B,C,D, whose faces are marked with [0,0,4,4,4,4], [3,3,3,3,3,3],[2,2,2,2,6,6],[1,1,1,5,5,5] respectively, where die A beats…
A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…
These notes contain a revisit to the matrix construction of the Weil representation by the author in the Journal of Algebra in 1972.