Geodesic
The magnitude of odd balls via Hankel determinants of reverse Bessel polynomials
Discrete analysis (2020) Cet article a éte moissonné depuis la source Scholastica

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Magnitude is an invariant of metric spaces with origins in category theory. Using potential theoretic methods, Barceló and Carbery gave an algorithm for calculating the magnitude of any odd dimensional ball in Euclidean space, and they proved that it was a rational function of the radius of the ball. In this paper an explicit formula is given for the magnitude of each odd dimensional ball in terms of a ratio of Hankel determinants of reverse Bessel polynomials. This is done by finding a distribution on the ball which solves the weight equations. Using Schröder paths and a continued fraction expansion for the generating function of the reverse Bessel polynomials, combinatorial formulae are given for the numerator and denominator of the magnitude of each odd dimensional ball. These formulae are then used to prove facts about the magnitude such as its asymptotic behaviour as the radius of the ball grows.
Publié le : 
@article{DAS_2020_a13,
     author = {Simon Willerton},
     title = {The magnitude of odd balls via {Hankel} determinants of reverse {Bessel} polynomials},
     journal = {Discrete analysis},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2020_a13/}
}
TY  - JOUR
AU  - Simon Willerton
TI  - The magnitude of odd balls via Hankel determinants of reverse Bessel polynomials
JO  - Discrete analysis
PY  - 2020
UR  - http://geodesic.mathdoc.fr/item/DAS_2020_a13/
LA  - en
ID  - DAS_2020_a13
ER  - 
%0 Journal Article
%A Simon Willerton
%T The magnitude of odd balls via Hankel determinants of reverse Bessel polynomials
%J Discrete analysis
%D 2020
%U http://geodesic.mathdoc.fr/item/DAS_2020_a13/
%G en
%F DAS_2020_a13
Simon Willerton. The magnitude of odd balls via Hankel determinants of reverse Bessel polynomials. Discrete analysis (2020). http://geodesic.mathdoc.fr/item/DAS_2020_a13/