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The number of maximal sum free subsets of integers
... Cameron and ErdΛ os [6] raised the question of how many maximal sum-free sets there are in {1, . . . , n}, giving a lower bound of 2 bn/4c . In this paper we prove that there are in fact at most 2 ... See full document
11
Sharp bound on the number of maximal sum free subsets of integers
... the number of maximal sum-free subsets S of [n] with the property that (i) the smallest element of S is n/4 Β±o(n) and (ii) the second smallest element of S is at least n/2 β ...the ... See full document
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Cusp Forms in ππ(Ξπ(ππ)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant βππ
... Letter to the Editor Cusp Forms in S4 Ξ0 47 and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant β47 BarΔ±sΜ§ Kendirli Depa[r] ... See full document
11
Finding the ring of integers and its algorithms in algebraic number theory
... algebraic number theory: given an algebraic number field K, determine its ring of integers ο ..."small" number fields K, such as number fields that are given as K= Q[X]/fQ[X], ... See full document
5
The Ordinal Interpretation of the Integers and Its Use in Number Theory
... The author recently published a paper which claimed that an ordinal inter- pretation of numbers had limited applicability for cryptography. A further examination of this subject, in particular to what extent an ordinal ... See full document
11
On the number of representations of certain integers as sums of eleven or thirteen squares
... free values of n were stated without proof by Eisenstein [9], [10]. These formulas were extended to all non-negative integers n (again without proof) by Smith [30]. The Paris Academy of Sciences, apparently ... See full document
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The number of subsets of integers with no k term arithmetic progression
... To see how they work, we give a quick overview of the proof of Theorem 1.2. We first apply the hypergraph container theorem (Corollary 2.2) to obtain a small collection of containers covering all k-AP-free sets in ... See full document
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Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields
... 1. Goldsmith. Pabst and Scott (5) proved a similar result without the property of being distinct units. The sum of unit of numbers of rings of quadratic field also discussed by Ashrafi and Vamos (6). Further ... See full document
5
Idempotent Factorizations of Square-free Integers
... positive integers n that admit idempotent factorizations n = p Β―q Β― such that Ξ»(n) β£ (p Β― β 1)(q Β― β 1), where Ξ» is the Carmichael lambda ...infinite number of n with idempotent factorizations containing ... See full document
10
On the existence of a non zero lower bound for the number of Goldbach partitions of an even integer
... even number, given by the sums of two prime addends, form the nonempty set for all integers 2n with 2 β€ n β€ 2Γ10 14 ...the number of Goldbach partitions of all even integers greater than or ... See full document
10
Some Polygonal Sum Labeling of Paths
... polygonal sum labeling if its vertices can be labeled by non -negative integers such that the induced edge labels obtained by the sum of the labels of end vertices are the first q polygonal ... See full document
5
Algorithm for Linear Number Partitioning into Maximum Number of Subsets
... The number partitioning problem is to decide whether a given multiset of integers can be partitioned into two "halves" of given cardinalities such that the discrepancy, the absolute value of the ... See full document
6
Three Fascinating Pairs
... Mathematics. Number theory, as a fundamental body of knowledge, has played a significant role in the development of ...of Number theory is elegant, beautiful and delightful. In fact, Number theory is ... See full document
9
How to Make a Mudsparkler
... the integers in S that satisfy J h8, 3i, h9, 5i K ...the number of moduli appearing in (C1)-(C44) which are not divisible by 5; and we set s = 1041, the number of moduli divisible by ...of ... See full document
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Fourier Coefficients of a Class of Eta Quotients of Weight 16 with Level 12
... 2012 Cusp Forms in S 4 Ξ 0 79 and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant -79.. 2012 Cusp Forms in S 4 Ξ 0 [r] ... See full document
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Tetrahedral and Pentatopic Sum Labeling of Graphs
... pentatopic sum la- beling if its vertices can be labeled by non negative integers such that the induced edge labels obtained by the sum of the labels of end vertices are the first q tetrahedral or ... See full document
5
Some Domination Parameters of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs
... are integers Then the total domination number of is given by where is the length of the longest stretch of consecutive integers in each of which shares a prime factor with ARITHMETIC GRAPH ... See full document
7
Small maximal sum free sets
... the number of sum-free sets in the integers (for example [2, 3]) and the density and number of sum-free sets in abelian groups (for example ...[4]). sum-free ... See full document
14
Three questions of Bertram on locally maximal sum free sets II
... complete sum-free sets. A complete sum-free set in a finite group G is a sum-free set S satisfying G = S βͺ SS ...Any sum-free set S with the property that S = S β 1 ... See full document
7
The number of maximal matchings in polyphenylene chains
... Case 1. Let β be a para-hexagon, so that β attaches at the vertex , as shown above in Figure [para_extremal_case]. We will denote the resulting graph as . To compute ( ), we will consider the vertex and apply Lemma 4.1 ... See full document
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