Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to col...

Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to col...

We present several elementary theorems, observations and questions related to the theme of congruences satisfied by binomial coefficients and factorials modulo primes (or prime powers) in the setting of polynomial ring over a finite field. When we look at the factorial of n or the binomial coefficient ‘n choose m’ in this setting, though the values are in a function field, n and m can be usual ...

We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to column-strict...

an estimation problem of the mean µ of an inverse gaussian distribution ig(µ, c µ) with known coefficient of variation c is treated as a decision problem with entropy loss function. a class of bayes estimators is constructed, and shown to include mrse estimator as its closure. two important members of this class can easily be computed using continued fractions

The Intraclass Correlation Coefficient (ICC) is commonly used to estimate the similarity between quantitative measures obtained from different sources. Overdispersed data is traditionally transformed so that linear mixed model (LMM) based ICC can be estimated. A common transformation used is the natural logarithm. The reliability of environmental sampling of fecal slurry on freestall pens has b...

This paper discusses an abelian group, also called a commutative under addition of the binomial coefficients combinatorial geometric series. The series is derived from multiple summations coefficient for each term in refers to coefficient. idea can enable scientific researchers solve real life problems.

This paper discusses a commutative group, ring, and field under addition multiplication of the binomial coefficients in combinatorial geometric series. The series is derived from multiple summations coefficient for each term refers to coefficient. idea can enable scientific researchers solve real life problems.