Unification of zero-sum problems, subset sums and covers of Z

作者：Sun ZW^*

来源：Electronic Research Announcements of the American Mathematical Society, 2003, 9: 51-60.

DOI：10.1090/S1079-6762-03-00111-2

• zero-sum
• subset sums
• covers of Z

In combinatorial number theory, zero-sum problems, subset sums and covers of the integers are three different topics initiated by P. Erdos and investigated by many researchers; they play important roles in both number theory and combinatorics. In this paper we announce some deep connections among these seemingly unrelated fascinating areas, and aim at establishing a unified theory! Our main theorem unifies many results in these three realms and also has applications in many aspects such as finite fields and graph theory. To illustrate this, here we state our extension of the Erdos-Ginzburg-Ziv theorem: If A = {alpha(s)(mod n(s))}(s=1)(k) covers some integers exactly 2p - 1 times and others exactly 2p times, where p is a prime, then for any c(1), ..., c(k) is an element of Z/pZ there exists an I subset of or equal to {1, ..., k} such that Sigma(sis an element ofI) 1/n(s) = p and Sigma(sis an element ofI) c(s) = 0.

• 出版日期2003
• 单位南京大学