Abstract

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Symmetry: Culture and Science
Volume 31, Number 4, pages 439-447 (2020)
https://doi.org/10.26830/symmetry_2020_4_439

EXTREME ASYMMETRY AND CHIRALITY A CHALLENGING QUANTIFICATION

Michel Petitjean^*

^* Université de Paris, BFA, CNRS UMR 8251, INSERM ERL U1133, F-75013 Paris, France.
E-pôle de Génoinformatique, CNRS UMR 7592, Institut Jacques Monod, 75013 Paris, France.
E-mail: petitjean.chiral@gmail.com, michel.petitjean@univ-paris-diderot.fr
Web: http://petitjeanmichel.free.fr/itoweb.petitjean.html
ORCID: 0000-0002-1745-5402.

Abstract: Symmetry operators must be defined relatively to a space and to a metric. Complex symmetries are typically considered in the case of the cartesian product of the Euclidean space by a space whose elements are tuples of colors. While interesting open problems exist in this field, challenging ones remain in the Euclidean case, without invoking colors. We present some of these problems in the case of extreme chirality figures and of extreme asymmetrical probability distributions.

Keywords: chirality, mirror symmetry, asymmetry, skewness.
MSC 2020: 51M16, 52A40, 60E15

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