1,174 research outputs found
Coincidences in numbers of graph vertices corresponding to regular planar hyperbolic mosaics
The aim of this paper is to determine the elements which are in two pairs of
sequences linked to the regular mosaics and on the
hyperbolic plane. The problem leads to the solution of diophantine equations of
certain types.Comment: 10 pages, 2 figures, Annales Mathematicae et Informaticae 43 (2014
The growing ratios of hyperbolic regular mosaics with bounded cells
In 3- and 4-dimensional hyperbolic spaces there are four, respectively five,
regular mosaics with bounded cells. A belt can be created around an arbitrary
base vertex of a mosaic. The construction can be iterated and a growing ratio
can be determined by using the number of the cells of the considered belts. In
this article we determine these growing ratios for each mosaic in a generalized
way.Comment: 17 pages, 3 figure
Fibonacci words in hyperbolic Pascal triangles
The hyperbolic Pascal triangle is a new
mathematical construction, which is a geometrical generalization of Pascal's
arithmetical triangle. In the present study we show that a natural pattern of
rows of is almost the same as the sequence consisting of
every second term of the well-known Fibonacci words. Further, we give a
generalization of the Fibonacci words using the hyperbolic Pascal triangles.
The geometrical properties of a imply a graph structure
between the finite Fibonacci words.Comment: 10 pages, 4 figures, Acta Univ. Sapientiae, Mathematica, 201
Alternating sums in hyperbolic Pascal triangles
A new generalization of Pascal's triangle, the so-called hyperbolic Pascal
triangles were introduced in [H.B, L.N, L.Sz: Hyperbolic Pascal triangles]. The
mathematical background goes back to the regular mosaics in the hyperbolic
plane. The alternating sum of elements in the rows was given in the special
case of the hyperbolic Pascal triangles. In this article, we
determine the alternating sum generally in the hyperbolic Pascal triangle
corresponding to with .Comment: 9 pages, 7 figure
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