This is a list of all the publications on magnitude of which I am aware.
Here I mean "magnitude" in the specific sense of these papers.
The criterion for inclusion is that the paper is specifically about
magnitude, or magnitude plays a major role in the work, rather than it merely
including a citation. I have included papers on magnitude for
ordinary categories, which is usually called Euler characteristic.
However, I have excluded papers on the diversity measures that are
closely related to magnitude, except those in which
magnitude is discussed explicitly.
Within each subject area, papers are ordered by arXiv date.
Magnitude (Euler characteristic) of ordinary categories:
The Euler characteristic of a category.
Documenta Mathematica 13 (2008), 21–49.
Clemens Berger and Tom Leinster.
The Euler characteristic of a category as the sum of a divergent
Homology, Homotopy and Applications 10 (2008), 41–51.
Martin Wedel Jacobsen and Jesper Møller.
Euler characteristics and Möbius algebras of p-subgroup
Journal of Pure and Applied Algebra 216 (2012), 2665–2696.
The Euler characteristic of acyclic categories.
Kyushu Journal of Mathematics 65 (2011), 85–99.
Notions of Möbius inversion.
Bulletin of the Belgian Mathematical Society—Simon Stevin
19 (2012), 911–935.
Euler characteristics of categories and barycentric subdivision.
Münster Journal of Mathematics 6 (2013), 85–116.
The zeta function of a finite category.
Documenta Mathematica 18 (2013), 1243–1274.
The zeta function of a finite category which has Möbius
The zeta function of a finite category and the series Euler
Euler characteristics of centralizer subcategories.
Čech complexes for covers of small categories.
Homology, Homotopy and Applications 19 (2017), 281–291.
Discrete Euler integration over functions on finite categories.
Topology and its Applications 204 (2016), 185–197.
Magnitude of higher categories:
The Euler characteristic of a bicategory and the product formula for
Magnitude of additive and linear categories:
Joseph Chuang, Alastair King, and Tom Leinster.
On the magnitude of a finite dimensional algebra.
Theory and Applications of Categories 31 (2016), 63–72.
Magnitude of graphs (excluding magnitude homology):
The magnitude of a graph.
Mathematical Proceedings of the Cambridge
Philosophical Society, to appear.
Magnitude of enriched categories generally (see also the paper "The
magnitude of metric spaces" below):
Kazunori Noguchi and Kohei Tanaka.
The Euler characteristic of an enriched category.
Theory and Applications of Categories 31 (2016), 1–30.
Magnitude of metric spaces:
Tom Leinster and Simon Willerton.
On the asymptotic magnitude of subsets of Euclidean space.
Geometriae Dedicata 164 (2013), 287–310.
A maximum entropy theorem with applications to the measurement of
Heuristic and computer calculations for the magnitude of metric spaces.
On the magnitude of spheres, surfaces and other homogeneous spaces.
Geometriae Dedicata 168 (2014), 291–310.
The magnitude of metric spaces.
Documenta Mathematica 18 (2013), 857–905.
Positive definite metric spaces.
Positivity 17 (2013), 733–757.
Spread: a measure of the size of metric spaces.
International Journal of Computational Geometry and Applications
25 (2015), 207–225.
Magnitude, diversity, capacities, and dimensions of metric spaces.
Potential Analysis 42 (2015), 549–572.
Juan Antonio Barceló and Anthony Carbery.
On the magnitudes of compact sets in Euclidean spaces.
American Journal of Mathematics 140 (2018), 449–494.
Tom Leinster and Mark Meckes.
Maximizing diversity in biology and beyond.
Entropy 18 (2016), article 88.
Tom Leinster and Mark Meckes.
The magnitude of a metric space: from category theory to geometric measure
in Nicola Gigli
Measure Theory in Non-Smooth Spaces, de Gruyter Open, 2017.
Heiko Gimperlein and Magnus Goffeng.
On the magnitude function of domains in Euclidean space.
The magnitude of odd balls via Hankel determinants of reverse Bessel
On the magnitude of odd balls via potential functions.
Richard Hepworth and Simon Willerton.
Categorifying the magnitude of a graph.
Homology, Homotopy and Applications 19 (2017), 31–60.
Tom Leinster and Michael Shulman.
Magnitude homology of enriched categories and metric spaces.
Ryuki Kaneta and Masahiko Yoshinaga.
Magnitude homology of metric spaces and order complexes.
On the magnitude homology of metric spaces.
Magnitude meets persistence. Homology theories for filtered simplicial
Smoothness filtration of the magnitude complex.
Graph magnitude homology via algebraic Morse theory.
This page was last changed on 15 November 2018.