## Jerzy Kocik

Talks Back to the main page

## Papers and preprints organized by subject

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

## Apolloniana

Apollonian disk packings: geometry, number theory, physics.

A note on unbounded Apollonian disk packings

[arXiv:1910.05924]

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),

arXiv:1909.06994

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

[arXiv:1807.06773]

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,

arXiv:1201.2067

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

[pdf]

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

[pdf]

Lens sequences(2007),

arXiv:0710.3226.

A theorem on circle configurations(2007).

arXiv:0706.0372,

Clifford algebras and Euclid's parameterization of Pythagorean triples,Advances in Applied Clifford Algebras (Mathematical Structures),172007 pp. 71-93.

[pdf]

## Relativity

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

[arXiv:1910.06556]

Making sense of relativistic composition of velocities

[arXiv:1910.06785]

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 201280(8) p. 737. [pdf]

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

[arXiv:1408.1493]

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

[pdf]

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

[arXiv:1709.06284]

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

[arXiv:1604.00109]

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

[pdf]

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)

[pdf]

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 PhysikVol. 52 (4) 2004, pp. 343-359.

[pdf]

Berezin quantization of the Schroedinger algebra(with P. Feinsilver and R. Schott)Infinite-Dimensional Analysis: QP,61, 2003, pp. 57-71. [pdf]

Krawtchouk matrices from classical and quantum walks(with P. Feinsilver)Contemporary Mathematics,2872002 , pp. 83-96.

[pdf].

Canonical variables and analysis on so(n,2)(with M. Giering and P. Feinsilver),Journal of Physics: A Mathematical,342001 pp 2367--2376.

[pdf]

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.

[pdf]

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

[pdf]

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.,22007, 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.

[pdf]

This paper received theLester Ford Awardfrom the Mathematical Association of America.

Simpson's paradox: proof without words.[light matters]Mathematics Magazine742001 (Dec).

[pdf]

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