Add to ORKG© 2017 In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q2 and Q4 of Cusick and Li (2005). We next find several bounds for the number of nontrivial bisections and further compute (using a supercomputer) the exact number of such bisections for n≤51
A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two...
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials th...
We give a conjecture on the set of numbers that occurs at least 6 times in the Pascal Triangle. We d...
In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously...
© 2018 In this paper, we present an algorithm which allows us to search for all the bisections for t...
In this note we present several unusual problems involving divisibility of the binomial coefficients...
Abstract. Much is known about binomial coefficients where primes are con-cerned, but considerably le...
A practical number is a positive integer n such that every positive integer less than n can be writt...
This paper presents a theorem on the binomial coefficients of combinatorial geometric series and its...
AbstractWe investigate lower bounds for ω((sn)) − ω((rn)) that are independent of n. This difference...
Let s and t be variables. Define polynomials {n} in s, t by {0} = 0, {1} = 1, and {n} = s {n − 1}+...
Abstract. In 1947 Fine obtained an expression for the number ap(n) of bi-nomial coefficients on row ...
A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two...
The primary goal of this paper is to achieve a simple generalization on binomial coefficients for al...
We investigate when the sequence of binomial coefficients binom(k,i) modulo a prime p, for a fixed p...
A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two...
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials th...
We give a conjecture on the set of numbers that occurs at least 6 times in the Pascal Triangle. We d...
In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously...
© 2018 In this paper, we present an algorithm which allows us to search for all the bisections for t...
In this note we present several unusual problems involving divisibility of the binomial coefficients...
Abstract. Much is known about binomial coefficients where primes are con-cerned, but considerably le...
A practical number is a positive integer n such that every positive integer less than n can be writt...
This paper presents a theorem on the binomial coefficients of combinatorial geometric series and its...
AbstractWe investigate lower bounds for ω((sn)) − ω((rn)) that are independent of n. This difference...
Let s and t be variables. Define polynomials {n} in s, t by {0} = 0, {1} = 1, and {n} = s {n − 1}+...
Abstract. In 1947 Fine obtained an expression for the number ap(n) of bi-nomial coefficients on row ...
A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two...
The primary goal of this paper is to achieve a simple generalization on binomial coefficients for al...
We investigate when the sequence of binomial coefficients binom(k,i) modulo a prime p, for a fixed p...
A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two...
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials th...
We give a conjecture on the set of numbers that occurs at least 6 times in the Pascal Triangle. We d...