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 of categories, which is
usually called Euler characteristic. However, I have not included papers on
the diversity measures that are closely related to magnitude, except for
those in which magnitude is discussed explicitly.
Within each topic, papers are ordered by arXiv date. I'll add journal
publication details as I learn them and would be happy to hear of any
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 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.
American Journal of Mathematics, to appear.
The magnitude of odd balls via Hankel determinants of reverse Bessel
Analysis 2020, number 5.
On the magnitude of odd balls via potential functions.
On the magnitude and intrinsic volumes of a convex body in Euclidean
Mathematika 66 (2020), 343–355.
Glenn Fung, Eric Bunch and Dan Dickinson.
Approximating the convex hull via metric space magnitude.
Tom Leinster and Emily Roff.
The maximum entropy of a metric space.
2019; Quarterly Journal of Mathematics, to appear.
Eric Bunch, Daniel Dickinson, Jeffery Kline and Glenn Fung.
Practical applications of metric space magnitude and weighting
Entropy and Diversity: The Axiomatic Approach.
Cambridge University Press, 2021.
Eric Bunch, Jeffery Kline, Daniel Dickinson, Suhaas Bhat and Glenn
Weighting vectors for machine learning: numerical harmonic analysis applied
to boundary detection.
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 166 (2019), 247–264.
Richard Hepworth and Simon Willerton.
Categorifying the magnitude of a graph.
Homology, Homotopy and Applications 19(2) (2017), 31–60.
Tom Leinster and Michael Shulman.
Magnitude homology of enriched categories and metric spaces.
Algebraic & Geometric Topology, to appear.
Ryuki Kaneta and Masahiko Yoshinaga.
Magnitude homology of metric spaces and order complexes.
Bulletin of the London Mathematical Society 53(3) (2021), 893–905
On the magnitude homology of metric spaces.
Magnitude meets persistence. Homology theories for filtered simplicial
The homology of data.
PhD thesis, University of Oxford, 2018.
Smoothness filtration of the magnitude complex.
Forum Mathematicum 32 (2020), 625–639.
Graph magnitude homology via algebraic Morse theory.
Magnitude homology of geodesic space.
Magnitude homology of geodesic metric spaces with an upper curvature
Algebraic & Geometric Topology 21 (2021), 647–664.
Torsion in the Khovanov homology of links and the magnitude homology of
PhD thesis, North Carolina State University, 2019.
Quantales, persistence, and magnitude homology.
Dejan Govc and Richard Hepworth.
Journal of Pure and Applied Algebra 225 (2021), 106517.
Radmila Sazdanovic and Victor Summers.
Torsion in the magnitude homology of graphs.
Yasuhiko Asao and Kengo Izumihara.
Geometric approach to graph magnitude homology.
Rémi Bottinelli and Tom Kaiser.
Magnitude homology, diagonality, medianness, Künneth and
Yasuhiko Asao, Yasuaki Hiraoka and Shu Kanazawa.
Girth, magnitude homology, and phase transition of diagonality.
This page was last changed on 3 September 2021.