Bicovariograms and Euler characteristic of regular sets

Regular maps and hypermaps of Euler characteristic -1 to -200

This paper describes the determination of all orientably-regular maps and hypermaps of genus 2 to 101, and all non-orientable regular maps and hypermaps of genus 3 to 202. It extends the lists obtained by Conder and Dobcsányi (2001) of all such maps of Euler characteristic −1 to −28, and corrects errors made in those lists for the vertexor face-multiplicities of 14 ‘cantankerous’ non-orientable...

Orientably regular maps with Euler characteristic divisible by few primes

Let G be a (2,m, n)-group and let x be the number of distinct primes dividing χ, the Euler characteristic of G. We prove, first, that, apart from a finite number of known exceptions, a nonabelian simple composition factor T of G is a finite group of Lie type with rank n ≤ x. This result is proved using new results connecting the prime graph of T to the integer x. We then study the particular ca...

Exponentiation and Euler Characteristic

The Euler Characteristic

I will describe a few basic properties of the Euler characteristic and then I use them to prove special case of a cute formula due to Bernstein-Khovanskii-Koushnirenko. 1. Basic properties of the Euler characteristic The Euler characteristic is a function χ which associates to each reasonable topological space X an integer χ(X). For us a reasonable space would be a space which admits a finite s...

Local maxima and the expected Euler characteristic of excursion sets of χ, F and t fields

The maximum of a Gaussian random field was used by Worsley et al. (1992) to test for activation at an unknown point in positron emission tomography images of blood flow in the human brain. The Euler characteristic of excursion sets was used as an estimator of the number of regions of activation. The expected Euler characteristic of excursion sets of stationary Gaussian random fields has been de...