Here is the gist of the Eisenbud–Sturmfels paper Binomial ideals, Duke Math. J. 84 (1996), 1–45. The main results are that the associated primes, the primary components, and the radical of a binomial ideal in a polynomial ring are binomial if the base ring is algebraically closed. Throughout, R = k[X1, . . . , Xn], where k is a field and X1, . . . , Xn are variables over k. A monomial is an ele...

BACKGROUND The beta-binomial model is one of the methods that can be used to validly combine event rates from overdispersed binomial data. Our objective is to provide a full description of this method and to update and broaden its applications in clinical and public health research. METHODS We describe the statistical theories behind the beta-binomial model and the associated estimation metho...

For >40 years, geneticists and science historians have appealed to the tetrad-pollen model as an explanation of the bias toward expectation in Mendel's data, albeit without experimental support. Our experiments demonstrate that pollen sampling during self-pollination in pea conforms to the binomial distribution with no evidence of a tetrad-pollen effect.

Tuenter considered centered binomial sums of the form Sr(n) = 2n ∑

In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.