Browsing by Author "Calkin, Neil J."
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Almost Odd Random SumFree Sets
Calkin, Neil J.; Cameron, P. J. (Georgia Institute of Technology, 199507)We show that if S_1 is a strongly complete sumfree set of positive integers, and if S_0 is a finite sumfree set, then with positive probability a random sumfree set U contains S_0 and is contained in S_0\cup S_1. As ... 
Counting Sets of Integers, No k of Which Sum to Another
Calkin, Neil J.; Taylor, Angela C. (Georgia Institute of Technology, 199507)We show that for every k greater or equal than 3 the number of subsets of {1,2,...,n} containing no solution to x_1 + x_2 + ... + x_k = y, where the x_i need not be distinct, is at most c2^{\alpha n}, where \alpha = (k1)/k. 
A Curious Binomial Identity
Calkin, Neil J. (Georgia Institute of Technology, 20091207)In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients. 
Dependent Sets of Constant Weight Binary Vectors
Calkin, Neil J. (Georgia Institute of Technology, 199507)We determine lower bounds for the number of random binary vectors, chosen uniformly from vectors of weight k, needed to obtain a dependent set. 
New Ramsey Bounds from Cyclic Graphs of Prime Order
Calkin, Neil J.; Erdös, Paul; Tovey, Craig A. (Georgia Institute of Technology, 199509)We present new explicit lower bounds for some Ramsey numbers. All the graphs are cyclic, and are on a prime number of vertices. We give a partial probabilistic analysis which suggests that the cyclic Ramsey numbers grow ... 
The Number of Independent Sets in a Grid Graph
Calkin, Neil J.; Wilf, Herbert S. (Georgia Institute of Technology, 199507) 
On a Class of Aperiodic SumFree Sets
Calkin, Neil J.; Erdös, Paul (Georgia Institute of Technology, 199410)We show that certain natural aperiodic sumfree sets are incomplete that is that there are infinitely many n not in S which are not a sum of two element of S. 
Some Conditions on Periodicity for SumFree Sets
Calkin, Neil J.; Finch, Steven R. (Georgia Institute of Technology, 199507)Cameron has introduced a natural bijection between the set of one way in nite binary sequences and the set of sumfree sets (of positive integers), and observed that a sumfree set is ultimately periodic only if the ...