Jerzy Kocik

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Papers and preprints organized by subject

  • → Strongly related to the subject.
  • → Weakly related.


Apollonian disk packings: geometry, number theory, physics.

  • A note on unbounded Apollonian disk packings

  • Tessellations and Descartes disk configurations
    [ arXiv:1910.05919 ]

  • Apollonian coronas and a new Zeta function (2019),
    [ arXiv:1909.09941]

  • Spinors and the Descartes configuration of circles (2019),

  • Coupled-ring resonance and unitary groups (with M. Sayeh), The Journal of the Optical Society of America B, 36 (3), 2019, 667-673.

  • Skein relations for spin networks, modified, Journal of Knot Theory and Its Ramifications, 27 (7) 2018
    [arXiv:1807.07244 ]

  • The Koide Lepton Mass Formula and Geometry of Circle Configurations,

  • On a Diophantine equation that generates all integral Apollonian gaskets, , ISRN Geometry. Article ID 348618, 19 pages, 2012. doi:10.5402/2012/348618.

  • Golden Window [light matters] (2010), Mathematics Magazine, 83 (5) 2010, no. 5, pp. 228-237.

  • Lens sequences (2007),

  • A theorem on circle configurations (2007).

  • Clifford algebras and Euclid's parameterization of Pythagorean triples, Advances in Applied Clifford Algebras (Mathematical Structures), 17 2007 pp. 71-93.


  • The loop of relativistic velocities as a deformation of the menhir loop

  • Making sense of relativistic composition of velocities

  • Cromlech, menhirs and celestial sphere: an unusual representation of the Lorentz group,
    [ arXiv:1604.05698 ]

  • Geometric diagram for relativistic addition of velocities, Am. J. Phys. Aug 2012 80 (8) p. 737. [pdf]

  • A Porism Concerning Cyclic Quadrilaterals, Geometry, Volume 2013 (Jun 2013), Article ID 483727.

  • Structure of matrix manifolds and a particle model (with J. Rzewuski), Journal of Mathematical Physics, 37 (2), 1996, pp. 1004-28.

  • On projections of spinor spaces onto Minkowski space (with J. Rzewuski), in "Symmetries in Science II," (B. Gruber, ed.), Plenum, New York, 1986.

Lie algebras and mathematical physics

  • Casimir energy of Sierpinski triangles (with K.V. Shajesh, P. Parashar, I. Cavero-Pelaez, and I. Brevik), Phys. Rev. D, 96, Nov 2017, eid 105010

  • Krawtchouk matrices from the Feynman path integral and from the split quaternions, Contemporary Mathematics, 668, 2016, pp . 131-164.

  • Canonical endomorphism field on a Lie algebra, Journal of Generalized Lie Theory and Applications, 4 Oct 2010, article ID G100302.

  • Traces, symmetric functions, and a raising operator: Generating function for Cauchy's enumeration formula, Proc. of the Fifth Intern. Workshop on Appl. Category Theory, Graph-Operad-Logic, Merida, May 2006 (to appear)

  • Krawtchouk polynomials and Krawtchouk matrices, (with P. Feinsilver), Recent Advances in Applied Probability, R. Baeza-Yates et al. (eds), Springer Verlag, 2005, pp. 115-143.
    [pdf], [arXiv:quant-ph/0702073]

  • Representations of the Schroedinger algebra and Appell systems (with P. Feinsilver and R. Schott) Fortschritte der Physik Vol. 52 (4) 2004, pp. 343-359.

  • Berezin quantization of the Schroedinger algebra (with P. Feinsilver and R. Schott) Infinite-Dimensional Analysis: QP, 6 1, 2003, pp. 57-71. [pdf]

  • Krawtchouk matrices from classical and quantum walks (with P. Feinsilver) Contemporary Mathematics, 287 2002 , pp. 83-96.

  • Canonical variables and analysis on so(n,2) (with M. Giering and P. Feinsilver), Journal of Physics: A Mathematical, 34 2001 pp 2367--2376.

  • Duplex numbers, diffusion systems, and generalized quantum mechanics, International Journal for Theoretical Physics, 38 (8) 1999 (Aug), pp. 2219-28. [pdf]

  • The geometry of elastic collisions and Heron's law, American Journal of Physics, 67 (6) 1999, pp. 516-19.

  • Representations and stochastic processes on groups of type H (with P. Feinsilver and R. Schott), Journal of Functional Analysis, 115, 1993, 146-165.

  • Representation of the Heisenberg algebra, Riccati systems, and associated geometric structures, (with P. Feinsilver), Proceedings of the Conference on Differential Geometric Methods in Physics, Claustal, 1986.

  • On geometry of phenomenological thermodynamics, in "Symmetries in Science II," (B.Gruber, ed.), Plenum, New York, 1986.
    [arXiv:1807.08908 [math-ph]]

Discrete math

  • Harmonic evolutions on graphs, Int. J. Math. and Comp. Sci., 2 2007, no. 1, pp. 65-82.
    [pdf]. [arXiv:1201.1355 [math.CO]}

  • Mathematics of the English tense system, Preprint of UIUC, 1998.
    [pdf coming soon]

General math and creative contributions

  • Disentangling a triangle [light maters] (with A. Solecki), Am. Math. Monthly, 116 (3), March 2009, pp 228-237.
    This paper received the Lester Ford Award from the Mathematical Association of America.

  • Simpson's paradox: proof without words. [light matters] Mathematics Magazine 74 2001 (Dec).

  • On the Crossroads of Time, or Mismeasurement of Tense, ToBe (Polish American Academic Quarterly), Vol. 1, No 1, September 1993, pp. 18-24.

  • Entries in the Online Encyclopedia of Integer Sequences: nid:A181106

  • Two article-entries in the "Encyclopedia of Supersymmetry" (1) Riemann Sphere, (2) Poisson Bracket. (J. Bagger, S. Duplij, W. Siegel, eds.), Kluwer, Dec 2003.

Other creative contributions

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