
Let
Hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we introduce and study Fibonacci-Pell hybrinomials, i.e. polynomials, which are a generalization of hybrid numbers of the Fibonacci type.
The hub-integrity of a graph is given by the minimum of
A graph
The sums
In a series of former papers, we obtained limit functions which describe scaling properties of the Farey sequence of order
Bulgarian solitaire is played on
For the special case
We introduce a polygonal cylinder
In this paper we find recurrence relations for the asymptotic probability a vertex is
Binomial coefficients of the form
In this paper, we analyze the stochastic properties of some large size (area) polyominoes’ perimeter such that the directed column-convex polyomino, the columnconvex polyomino, the directed diagonally-convex polyomino, the staircase (or parallelogram) polyomino, the escalier polyomino, the wall (orbargraph) polyomino. All polyominoes considered here are made of contiguous, not-empty columns, without holes, such that each column must be adjacent to some cell of the previous column. We compute the asymptotic (for large size n) Gaussian distribution of the perimeter, including the corresponding Markov property of the chain of columns, and the convergence to classical Brownian motions of the perimeter seen as a trajectory according to the successive columns. All polyominoes of size n are considered as equiprobable.
Convolution conditions are discussed for the
we discuss a framework for constructing large subsets of
Let
In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize Laguerre polynomials and associated Lah polynomials. We discuss, for these polynomials, their explicit expressions, relations to the successive derivatives of a given function, real zeros and recurrence relations. Some known results are significantly simplified.
We show that if
1970-2025 CP (Manitoba, Canada) unless otherwise stated.