Binomial Coefficient Predictors
نویسنده
چکیده
For a prime p and nonnegative integers n, k, consider the set A (p) n,k = {x ∈ [0, 1, ..., n] : p|| ( n x ) }. Let the expansion of n + 1 in base p be n + 1 = α0p ν + α1p ν−1 + · · · + αν , where 0 ≤ αi ≤ p − 1, i = 0, . . . , ν. Then n is called a binomial coefficient predictor in base p(p-BCP), if |A (p) n,k| = αkp , k = 0, 1, . . . , ν. We give a full description of the p-BCP’s in every base p.
منابع مشابه
The Negative q-Binomial
Interpretations for the q-binomial coefficient evaluated at −q are discussed. A (q, t)-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces. 1. The q-binomial The q-binomial coefficient is defined for integers k and n, with 0 ≤ k ≤ n, and an indeterminate q by
متن کاملCombinatorial Proofs of Some Moriarty-type Binomial Coefficient Identities
In this note, we present combinatorial proofs of some Moriarty-type binomial coefficient identities using linear and circular domino arrangements.
متن کاملCombinatorial proofs of a kind of binomial and q-binomial coefficient identities
We give combinatorial proofs of some binomial and q-binomial identities in the literature, such as ∞ ∑ k=−∞ (−1)kq(9k2+3k)/2 [ 2n n + 3k ] = (1 + q) n−1 ∏ k=1 (1 + q + q) (n ≥ 1),
متن کاملDivisors of the Middle Binomial Coefficient
We study some old and new problems involving divisors of the middle binomial coefficient (2n n ) .
متن کاملComparison of five introduced confidence intervals for the binomial proportion
So far many confidence intervals were introduced for the binomial proportion. In this paper, our purpose is comparing five well known based on their exact confidence coefficient and average coverage probability.
متن کامل