The Inverse Erdős-Heilbronn Problem

The Inverse Erdös-Heilbronn Problem

The famous Erdős-Heilbronn conjecture (first proved by Dias da Silva and Hamidoune in 1994) asserts that if A is a subset of Z/pZ, the cyclic group of the integers modulo a prime p, then |A +̂ A| > min{2 |A| − 3, p}. The bound is sharp, as is shown by choosing A to be an arithmetic progression. A natural inverse result was proven by Karolyi in 2005: if A ⊂ Z/pZ contains at least 5 elements and |...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Linear Extension of the Erdős - Heilbronn Conjecture 3

The famous Erdős-Heilbronn conjecture plays an important role in the development of additive combinatorial number theory. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erdős-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements a1, . . . , an of F , we have |{a1x1 + · · ·+ anxn : x1, . . . , xn ∈ A, and xi 6= xj if i 6= ...

Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture

0080 a New Extension of the Erdős - Heilbronn Conjecture

In 1964 P. Erdős and H. Heilbronn [EH] made the following challenging conjecture: If p is a prime, then for any subset A of the finite field Z/pZ we have |{x1 + x2 : x1, x2 ∈ A and x1 6= x2}| > min{p, 2|A| − 3}. It had remained open for thirty years until it was confirmed fully by Dias da Silva and Hamidoune [DH] who actually obtained the following generalization with help of the representation...