SET Addition of Amines to Alkenes

2003 ◽  
Author(s):  
Frederick Lewis ◽  
Elizabeth Crompton
Keyword(s):  
Set Addition

scholarly journals Restricted set addition in groups, II. A generalization of the Erdős-Heilbronn conjecture

10.37236/1482 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Vsevolod F. Lev
Keyword(s):  
General Type ◽  
Sharp Estimate ◽  
Abelian Groups ◽  
Polynomial Method ◽  
Set Addition

In 1980, Erdős and Heilbronn posed the problem of estimating (from below) the number of sums $a+b$ where $a\in A$ and $b\in B$ range over given sets $A,B\subseteq{\Bbb Z}/p{\Bbb Z}$ of residues modulo a prime $p$, so that $a\neq b$. A solution was given in 1994 by Dias da Silva and Hamidoune. In 1995, Alon, Nathanson and Ruzsa developed a polynomial method that allows one to handle restrictions of the type $f(a,b)\neq 0$, where $f$ is a polynomial in two variables over ${\Bbb Z}/p{\Bbb Z}$. In this paper we consider restricting conditions of general type and investigate groups, distinct from ${\Bbb Z}/p{\Bbb Z}$. In particular, for $A,B\subseteq{\Bbb Z}/p{\Bbb Z}$ and ${\cal R}\subseteq A\times B$ of given cardinalities we give a sharp estimate for the number of distinct sums $a+b$ with $(a,b)\notin\ {\cal R}$, and we obtain a partial generalization of this estimate for arbitrary Abelian groups.

scholarly journals Equality in Pollard's theorem on set addition of congruence classes

2007 ◽  
Vol 127 (1) ◽  
pp. 1-15 ◽  
Author(s):  
E. Nazarewicz ◽  
M. O'Brien ◽  
M. O'Neill ◽  
C. Staples
Keyword(s):  
Set Addition ◽  
Congruence Classes

scholarly journals A step beyond Freiman’s theorem for set addition modulo a prime

2020 ◽  
Vol 32 (1) ◽  
pp. 275-289
Author(s):  
Pablo Candela ◽  
Oriol Serra ◽  
Christoph Spiegel
Keyword(s):  
Set Addition ◽  
Freiman’S Theorem

THE ISOPERIMETRIC METHOD IN NON-ABELIAN GROUPS WITH AN APPLICATION TO OPTIMALLY SMALL SUMSETS

2008 ◽  
Vol 04 (06) ◽  
pp. 927-958 ◽  
Author(s):  
ÉRIC BALANDRAUD
Keyword(s):  
Number Theory ◽  
Abelian Group ◽  
Abelian Groups ◽  
Solvable Groups ◽  
Additive Number Theory ◽  
Alternating Groups ◽  
Additive Number ◽  
New Interpretation ◽  
Set Addition

Set addition theory is born a few decades ago from additive number theory. Several difficult issues, more combinatorial in nature than algebraic, have been revealed. In particular, computing the values taken by the function: [Formula: see text] where G is a given group does not seem easy in general. Some successive results, using Kneser's Theorem, allowed the determination of the values of this function, provided that the group G is abelian. Recently, a method called isoperimetric, has been developed by Hamidoune and allowed new proofs and generalizations of the classical theorems in additive number theory. For instance, a new interpretation of the isoperimetric method has been able to give a new proof of Kneser's Theorem. The purpose of this article is to adapt this last proof in a non-abelian group, in order to give new values of the function μG, for some solvable groups and alternating groups. These values allow us in particular to answer negatively a question asked in the literature on the μG functions.

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