In this paper, on one hand, we propose a new type of symmetric function to interpret the bi
$^{s} $ nomial coefficients and their analogs. On other hand, according to this function, we …

In this paper, we describe a method to determine the power sum of the elements of the rows
in the hyperbolic Pascal triangles corresponding to {4, q} with q≥ 5. The method is based on …

In this paper we study the problem of hyperball (hypersphere) packings in $3 $-dimensional
hyperbolic space. We introduce a new definition of the non-compact saturated ball packings …

In this paper, we describe the recurrence relation associated to the sum of diagonal
elements lying along a finite ray of certain type crossing the three-dimensional Pascal …

In this paper, we study congruent and noncongruent hyperball (hypersphere) packings to
the truncated regular cube and octahedron tilings. These are derived from the Coxeter …

Sažetak In this article we introduce a new type of Pascal pyramids. A regular squared
mosaic in the hyperbolic plane yields an\(h^{2} r\)-cube mosaic in space\(H^{2}\) xR and the …

In the present paper, we consider a variation of the hyperbolic Pascal pyramid where the
three leg-sequences (the constant 1 sequence) are replaced by the sequences {α n} n≥ …

In this article we introduce a new geometric object called hyperbolic Pascal simplex. This
newobject is presented by the regular hypercube mosaic in the 4-dimensional hyperbolic …

Here we summarize some results on a recently introduced new generalization of Pascal's
triangle called hyperbolic Pascal triangles. The name comes from the mathematical …

In this paper we study congruent and non-congruent hyperball (hypersphere) packings of
the truncated regular octahedron and cube tilings. These are derived from the Coxeter …