Related papers: Urn Models and Fibonacci Series

The paper considers urn schemes in which several urns can be involved. Simplified formulas are proposed that allow direct calculation of probabilities without the use of elements combinatorics.

We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has…

Urn models play an important role to express various basic ideas in probability theory. Here we extend this urn model with tubes. An urn contains coloured balls, which can be drawn with probabilities proportional to the numbers of balls of…

Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known,…

Consider the multicolored urn model where, after every draw, balls of the different colors are added to the urn in a proportion determined by a given stochastic replacement matrix. We consider some special replacement matrices which are not…

We prove some combinatorial identities using the Polya urn and the closely related Hoppe urn.

The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…

We introduce and discuss a special type of feedback interacting urn model with deterministic interaction. This is a generalisation of the very well known Eggenberger and Polya (1923) urn model. In our model, balls are added to a particular…

We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.

Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.

In this note, we obtain some identities for the generalized Fibonacci polynomial by using the Q(x) matrix. These identities including the Cassini identity and Honsberger formula can be applied to some polynomial sequences, such as Fibonacci…

We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.

We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…

We derive some Fibonacci and Lucas identities which contain inverse binomial coefficients. Extension of the results to the general Horadam sequence is possible, in some cases.

This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.

We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of them extending Cassini's identity for…

We establish some identities relating two sequences that are, as explained, related to the Tribonacci sequence. One of these sequences bears the same resemblance to the Tribonacci sequence as the Lucas sequence does to the Fibonacci…

We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the…

We study some properties of restricted and associated Fubini numbers. In particular, they have the natural extensions of the original Fubini numbers in the sense of determinants. We also introduce modified Bernoulli and Cauchy numbers and…