The Classical statistical inference for integer valued time-series has primarily been restricted to the integer valued autoregressive (INAR) process. Markov chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches of statistics and is particularly well suited to integer valued time-series where statistical inference is greatly assisted by data augmentation. Thus in ...

Let P (x) ∈ Z[x] be an integer-valued polynomial taking only positive values and let d be any fixed positive integer. The aim of this short note is to show, by elementary means, that for any sufficiently large integer N ≥ N0(P, d) there exists n such that P (n) contains exactly N occurrences of the block (q − 1, q − 1, . . . , q − 1) in its digital expansion in base q. The method of proof is co...

abstract. suppose g is an nvertex and medge simple graph with edge set e(g). an integervalued function f: e(g) → z is called a flow. tutte was introduced the flow polynomial f(g, λ) as a polynomial in an indeterminate λ with integer coefficients by f(g,λ) in this paper the flow polynomial of some dendrimers are computed.

Let p be a prime, and let f(x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum ∑ k≡r (mod pβ) (n k ) (−1)f (⌊ k − r pα ⌋) , where α > β > 0, n > pα−1 and r ∈ Z. This polynomial extension of Fleck’s congruence has various backgrounds and several consequences such as ∑ k≡r (mod pα) (n k ) a ≡ 0 ( mod p ⌊ n−pα−1 φ(pα) ...

Let p be a prime, and let f (x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum k≡r (mod p β) n k (−1) k f k − r p α , where α β 0, n p α−1 and r ∈ Z. This polynomial extension of Fleck's congruence has various backgrounds and several consequences such as k≡r (mod p α) n k a k ≡ 0 mod p n−p α−1 ϕ(p α) provided that ...

The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper, we introduce an modification of the INAR(1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structu...