AbstractGiven a linear recurrence integer sequence U = {un}, un+2 = un+1 + ur, n ⩾ 1, u1 = 1, u2> u1, we prove that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U. We give a graph theoretic interpretation of this result, study related problems and discuss possible generalizations
AbstractOne basic activity in combinatorics is to establish combinatorial identities by so-called ‘b...
AbstractIt is easy to deduce from Ramsey's theorem that given positive integers a1,a2,…,am and a fin...
Abstract. In this paper we prove that there exist infInitelv many disjoint sets of posItIve integers...
AbstractGiven a linear recurrence integer sequence U = {un}, un+2 = un+1 + ur, n ⩾ 1, u1 = 1, u2> u1...
Consider any set U = un with elements defined by un+2= un+2 + un, n ⩾ 1, where u1 and u2 are relativ...
Consider any set U = un with elements defined by un+2= un+2 + un, n ⩾ 1, where u1 and u2 are relativ...
For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the ...
AbstractThe principal result of this paper establishes the validity of a conjecture by Graham and Ro...
Partitions with gaps. Bijections between various restricted partitions of integers have been extensi...
AbstractWe characterize all numbers n and S with the following property: Every instance of the parti...
We give a possible explanation for the mystery of a missing number in the statement of a problem tha...
AbstractMacMahon [Combinatory Analysis, vols. I and II, Cambridge University Press, Cambridge, 1915,...
summary:Let $S$ be a non-empty subset of positive integers. A partition of a positive integer $n$ ...
summary:Let $S$ be a non-empty subset of positive integers. A partition of a positive integer $n$ ...
AbstractPartitions in which we use d(a) copies of each part a are studied. The results obtained here...
AbstractOne basic activity in combinatorics is to establish combinatorial identities by so-called ‘b...
AbstractIt is easy to deduce from Ramsey's theorem that given positive integers a1,a2,…,am and a fin...
Abstract. In this paper we prove that there exist infInitelv many disjoint sets of posItIve integers...
AbstractGiven a linear recurrence integer sequence U = {un}, un+2 = un+1 + ur, n ⩾ 1, u1 = 1, u2> u1...
Consider any set U = un with elements defined by un+2= un+2 + un, n ⩾ 1, where u1 and u2 are relativ...
Consider any set U = un with elements defined by un+2= un+2 + un, n ⩾ 1, where u1 and u2 are relativ...
For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the ...
AbstractThe principal result of this paper establishes the validity of a conjecture by Graham and Ro...
Partitions with gaps. Bijections between various restricted partitions of integers have been extensi...
AbstractWe characterize all numbers n and S with the following property: Every instance of the parti...
We give a possible explanation for the mystery of a missing number in the statement of a problem tha...
AbstractMacMahon [Combinatory Analysis, vols. I and II, Cambridge University Press, Cambridge, 1915,...
summary:Let $S$ be a non-empty subset of positive integers. A partition of a positive integer $n$ ...
summary:Let $S$ be a non-empty subset of positive integers. A partition of a positive integer $n$ ...
AbstractPartitions in which we use d(a) copies of each part a are studied. The results obtained here...
AbstractOne basic activity in combinatorics is to establish combinatorial identities by so-called ‘b...
AbstractIt is easy to deduce from Ramsey's theorem that given positive integers a1,a2,…,am and a fin...
Abstract. In this paper we prove that there exist infInitelv many disjoint sets of posItIve integers...
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