Magnitude: a bibliography


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 I've missed.

Magnitude (Euler characteristic) of ordinary categories:

  1. Tom Leinster.
    The Euler characteristic of a category.
    arXiv:math.CT/0610260; Documenta Mathematica 13 (2008), 21–49.
  2. Clemens Berger and Tom Leinster.
    The Euler characteristic of a category as the sum of a divergent series.
    arXiv:0707.0835; Homology, Homotopy and Applications 10 (2008), 41–51.
  3. Martin Wedel Jacobsen and Jesper Møller.
    Euler characteristics and Möbius algebras of p-subgroup categories.
    arXiv:1007.1890; Journal of Pure and Applied Algebra 216 (2012), 2665–2696.
  4. Kazunori Noguchi.
    The Euler characteristic of acyclic categories.
    arXiv:1004.2547; Kyushu Journal of Mathematics 65 (2011), 85–99.
  5. Tom Leinster.
    Notions of Möbius inversion.
    arXiv:1201.0413; Bulletin of the Belgian Mathematical Society—Simon Stevin 19 (2012), 911–935.
  6. Kazunori Noguchi.
    Euler characteristics of categories and barycentric subdivision.
    arXiv:1104.3630; Münster Journal of Mathematics 6 (2013), 85–116.
  7. Kazunori Noguchi.
    The zeta function of a finite category.
    arXiv:1203.6133; Documenta Mathematica 18 (2013), 1243–1274.
  8. Kazunori Noguchi.
    The zeta function of a finite category which has Möbius inversion.
    arXiv:1205.4380, 2012.
  9. Kazunori Noguchi.
    The zeta function of a finite category and the series Euler characteristic.
    arXiv:1207.6750, 2012.
  10. Jesper Møller.
    Euler characteristics of centralizer subcategories.
    arXiv:1502.01317, 2015.
  11. Kohei Tanaka.
    Čech complexes for covers of small categories.
    arXiv:1508.03688; Homology, Homotopy and Applications 19 (2017), 281–291.
  12. Kohei Tanaka.
    Discrete Euler integration over functions on finite categories.
    arXiv:1508.06391; Topology and its Applications 204 (2016), 185–197.

Magnitude of enriched categories generally (see also the paper "The magnitude of metric spaces" below):

  1. Kazunori Noguchi and Kohei Tanaka.
    The Euler characteristic of an enriched category.
    arXiv:1405.3356; Theory and Applications of Categories 31 (2016), 1–30.

Magnitude of metric spaces:

  1. Tom Leinster and Simon Willerton.
    On the asymptotic magnitude of subsets of Euclidean space.
    arXiv:0908.1582; Geometriae Dedicata 164 (2013), 287–310.
  2. Tom Leinster.
    A maximum entropy theorem with applications to the measurement of biodiversity.
    arXiv:0910.0906, 2009.
  3. Simon Willerton.
    Heuristic and computer calculations for the magnitude of metric spaces.
    arXiv:0910.5500, 2009.
  4. Simon Willerton.
    On the magnitude of spheres, surfaces and other homogeneous spaces.
    arXiv:1005.4041, 2010; Geometriae Dedicata 168 (2014), 291–310.
  5. Tom Leinster.
    The magnitude of metric spaces.
    arXiv:1012.5857; Documenta Mathematica 18 (2013), 857–905.
  6. Mark Meckes.
    Positive definite metric spaces.
    arXiv:1012.5863; Positivity 17 (2013), 733–757.
  7. Simon Willerton.
    Spread: a measure of the size of metric spaces.
    arXiv:1209.2300; International Journal of Computational Geometry and Applications 25 (2015), 207–225.
  8. Mark Meckes.
    Magnitude, diversity, capacities, and dimensions of metric spaces.
    arXiv:1308.5407; Potential Analysis 42 (2015), 549–572.
  9. Juan Antonio Barceló and Anthony Carbery.
    On the magnitudes of compact sets in Euclidean spaces.
    arXiv:1507.02502; American Journal of Mathematics 140 (2018), 449–494.
  10. Tom Leinster and Mark Meckes.
    Maximizing diversity in biology and beyond.
    arXiv:1512.06314; Entropy 18 (2016), article 88.
  11. Tom Leinster and Mark Meckes.
    The magnitude of a metric space: from category theory to geometric measure theory.
    arXiv:1606.00095; in Nicola Gigli (ed.), Measure Theory in Non-Smooth Spaces, de Gruyter Open, 2017.
  12. Heiko Gimperlein and Magnus Goffeng.
    On the magnitude function of domains in Euclidean space.
    arXiv:1706.06839; American Journal of Mathematics, to appear.
  13. Simon Willerton.
    The magnitude of odd balls via Hankel determinants of reverse Bessel polynomials.
    arXiv:1708.03227; Discrete Analysis 2020, number 5.
  14. Simon Willerton.
    On the magnitude of odd balls via potential functions.
    arXiv:1804.02174, 2018.
  15. Mark Meckes.
    On the magnitude and intrinsic volumes of a convex body in Euclidean space.
    arXiv:1904.08923; Mathematika 66 (2020), 343–355.
  16. Glenn Fung, Eric Bunch and Dan Dickinson.
    Approximating the convex hull via metric space magnitude.
    arXiv:1908.02692, 2019.
  17. Tom Leinster and Emily Roff.
    The maximum entropy of a metric space.
    arXiv:1908.11184, 2019; Quarterly Journal of Mathematics, to appear.
  18. Eric Bunch, Daniel Dickinson, Jeffery Kline and Glenn Fung.
    Practical applications of metric space magnitude and weighting vectors.
    arXiv:2006.14063, 2020.
  19. Tom Leinster.
    Entropy and Diversity: The Axiomatic Approach.
    arXiv:2012.02113, 2020; Cambridge University Press, 2021.
  20. Eric Bunch, Jeffery Kline, Daniel Dickinson, Suhaas Bhat and Glenn Fung.
    Weighting vectors for machine learning: numerical harmonic analysis applied to boundary detection.
    arXiv:2106.00827, 2021.

Magnitude of higher categories:

  1. Kohei Tanaka.
    The Euler characteristic of a bicategory and the product formula for fibered bicategories.
    arXiv:1410.0248, 2014.

Magnitude of additive and linear categories:

  1. Joseph Chuang, Alastair King and Tom Leinster.
    On the magnitude of a finite dimensional algebra.
    arXiv:1505.04281; Theory and Applications of Categories 31 (2016), 63–72.

Magnitude of graphs (excluding magnitude homology):

  1. Tom Leinster.
    The magnitude of a graph.
    arXiv:1401.4623; Mathematical Proceedings of the Cambridge Philosophical Society 166 (2019), 247–264.

Magnitude (co)homology:

  1. Richard Hepworth and Simon Willerton.
    Categorifying the magnitude of a graph.
    arXiv:1505.04125; Homology, Homotopy and Applications 19(2) (2017), 31–60.
  2. Tom Leinster and Michael Shulman.
    Magnitude homology of enriched categories and metric spaces.
    arXiv:1711.00802, 2017; Algebraic & Geometric Topology, to appear.
  3. Ryuki Kaneta and Masahiko Yoshinaga.
    Magnitude homology of metric spaces and order complexes.
    arXiv:1803.04247; Bulletin of the London Mathematical Society 53(3) (2021), 893–905
  4. Benoît Jubin.
    On the magnitude homology of metric spaces.
    arXiv:1803.05062, 2018.
  5. Nina Otter.
    Magnitude meets persistence. Homology theories for filtered simplicial sets.
    arXiv:1807.01540, 2018.
  6. Nina Otter.
    The homology of data.
    PhD thesis, University of Oxford, 2018.
  7. Richard Hepworth.
    Magnitude cohomology.
    arXiv:1807.06832, 2018.
  8. Kiyonori Gomi.
    Smoothness filtration of the magnitude complex.
    arXiv:1809.06593; Forum Mathematicum 32 (2020), 625–639.
  9. Yuzhou Gu.
    Graph magnitude homology via algebraic Morse theory.
    arXiv:1809.07240, 2018.
  10. Kiyonori Gomi.
    Magnitude homology of geodesic space.
    arXiv:1902.07044, 2019.
  11. Yasuhiko Asao.
    Magnitude homology of geodesic metric spaces with an upper curvature bound.
    arXiv:1903.11794, 2019; Algebraic & Geometric Topology 21 (2021), 647–664.
  12. Victor Summers.
    Torsion in the Khovanov homology of links and the magnitude homology of graphs.
    PhD thesis, North Carolina State University, 2019.
  13. Simon Cho.
    Quantales, persistence, and magnitude homology.
    arXiv:1910.02905, 2019.
  14. Dejan Govc and Richard Hepworth.
    Persistent magnitude.
    arXiv:1911.11016, 2019; Journal of Pure and Applied Algebra 225 (2021), 106517.
  15. Radmila Sazdanovic and Victor Summers.
    Torsion in the magnitude homology of graphs.
    arXiv:1912.13483, 2019.
  16. Yasuhiko Asao and Kengo Izumihara.
    Geometric approach to graph magnitude homology.
    arXiv:2003.08058, 2020.
  17. Rémi Bottinelli and Tom Kaiser.
    Magnitude homology, diagonality, medianness, Künneth and Mayer–Vietoris.
    arXiv:2003.09271, 2020.
  18. Yasuhiko Asao, Yasuaki Hiraoka and Shu Kanazawa.
    Girth, magnitude homology, and phase transition of diagonality.
    arXiv:2101.09044, 2021.

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