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A partition of the Catalan numbers and enumeration of genealogical trees

100%

Schimming R.

Discussiones Mathematicae Graph Theory

1996

tom 16

nr 2

181-195

A special relational structure, called genealogical tree, is introduced; its social interpretation and geometrical realizations are discussed. The numbers $C_{n,k}$ of all abstract genealogical trees with exactly n+1 nodes and k leaves is found by means of enumeration of code words. For each n, the $C_{n,k}$ form a partition of the n-th Catalan numer Cₙ, that means $C_{n,1}+C_{n,2}+ ...+C_{n,n} = Cₙ$.

Connections between Romanovski and other polynomials

88%

Weber H.

Open Mathematics

2007

tom 5

nr 3

581-595

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.

Limit theorems for number of diffusion processes, which did not absorb by boundaries

75%

Fedullo A., Gasanenko V.

Open Mathematics

2006

tom 4

nr 4

624-634

We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.

Ograniczanie wyników

2 Open Mathematics

1 Discussiones Mathematicae Graph Theory

1 Fedullo A.

1 Gasanenko V.

1 Schimming R.

1 Weber H.

1 2007

1 2006

1 1996

Wyniki wyszukiwania

A partition of the Catalan numbers and enumeration of genealogical trees

Connections between Romanovski and other polynomials

Limit theorems for number of diffusion processes, which did not absorb by boundaries