I. Up to our knowledge-since about 126 years we were lacking of classical type combinatorial interpretation of Fibonomial coefficients as it was Lukas [1]-to our knowledge-who was the first who had defined Finono-mial coefficients and derived a recurrence for them (see Historical Note in [2]). Namely as accurately noticed by Knuth and Wilf in [3] the recurrent relations for Fibonomial coefficie...

Letting B n (x) the n-th Bell polynomial, it is well known that B n admit specific integer coordinates in the two following bases x i numbers and binomial coefficients. Our aim is to prove that, for r + s = n, the sequence x j B k (x) is a family of bases of the Q-vectorial space formed by polynomials of Q [X ] for which B n admits a Binomial Recurrence Coefficient.

3 Data Generation 4 3.1 Bernoulli Observation Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Gaussian Observation Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 Poisson Observation Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.4 Negative-Binomial Observation Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Partial fraction decomposition method is applied to evaluate a general determinant of shifted factorial fractions, which contains several Gaussian binomial determinant identities .

We give a q-analogue of some binomial coefficient identities of Y. Sun [Electron.

0; n < m for n and m non-negative integers. Binomial coefficients play an important role in many areas of mathematics, including number theory, statistics and probability. Reciprocal binomial coefficients are also prolific in the mathematical literature and many results on reciprocals of binomial coefficient identities may be seen in the papers of Mansour [1], Pla [2], Rockett [3], Sury [5], Su...