20 citations · 84 across the 35 of their papers we have counts for
35 papers
Integral spinors, Apollonian disk packings, and Descartes groups
Jerzy Kocik
We show that every irreducible integral Apollonian packing can be set in the Euclidean space so that all of its tangency spinors and all reduced coordinates and co-curvatures are i…
Lucas, Fibonacci, and Chebyshev polynomials from matrices
Jerzy Kocik
A simple matrix formulation of the Fibonacci, Lucas, Chebyshev, and Dixon polynomials polynomials is presented. It utilizes the powers and the symmetric tensor powers of a certain…
Apollonian depth, spinors, and the super-Dedekind tessellation
Jerzy Kocik
The configuration space of tricycles (triples of disks in contact) is shown to coincide with the complex plane resulting as a projective space costructed from the tangency and Paul…
Induced orders in free monoids of words
Jerzy Kocik
A family of partial orders in the free monoid of words, induced from a partial order in alphabet, is presented. The induced orders generalize the chronological posets that have bee…
On a Diophantine equation that generates all integral Apollonian Gaskets
Jerzy Kocik
A remarkably simple Diophantine quadratic equation is known to generate all Apollonian integral gaskets (disk packings). A new derivation of this formula is presented here based on…
Traces, symmetric functions, and a raising operator
Jerzy Kocik
The polynomial relationship between elementary symmetric functions (Cauchy enumeration formula) is formulated via a ``raising operator" and Fock space construction. A simple graphi…