ZERO-SUM PROBLEMS FOR ABELIAN p-GROUPS AND COVERS OF THE INTEGERS BY RESIDUE CLASSES

نویسندگان

  • Zhi-Wei Sun
  • ZHI-WEI SUN
چکیده

Abstract. Zero-sum problems for abelian groups and covers of the integers by residue classes, are two different active topics initiated by P. Erdős more than 40 years ago and investigated by many researchers separately since then. In an earlier announcement [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author claimed some surprising connections among these seemingly unrelated fascinating areas. In this paper we establish further connections between zero-sum problems for abelian p-groups and covers of the integers. For example, we extend the famous Erdős-Ginzburg-Ziv theorem in the following way: If {as(mod ns)}ks=1 covers each integer either exactly 2q−1 times or exactly 2q times where q is a prime power, then for any c1, . . . , ck ∈ Z/qZ there exists an I ⊆ {1, . . . , k} such that P

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ZERO-SUM PROBLEMS IN ABELIAN p-GROUPS AND COVERS OF THE INTEGERS BY RESIDUE CLASSES

Abstract. Zero-sum problems in abelian groups and covers of the integers by residue classes, are two different active topics initiated by P. Erdős more than 40 years ago and investigated by many researchers separately since then. In an earlier announcement [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author claimed some surprising connections among these seemingly unrelated fa...

متن کامل

A Unified Theory of Zero - Sum Problems , Subset Sums and Covers of Z

Abstract. Zero-sum problems on abelian groups, subset sums in a field and covers of the integers by residue classes, are three different active topics initiated by P. Erdős and investigated by many researchers. In an earlier paper [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author announced some connections among these seemingly unrelated fascinating areas. In this paper we e...

متن کامل

A Unified Theory of Zero - Sum Problems , Subset Sums and Covers

Abstract. Zero-sum problems on abelian groups, subset sums in a field and covers of the integers by residue classes, are three different active topics initiated by P. Erdős more than 40 years ago and investigated by many researchers separately since then. In an earlier announcement [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author claimed some connections among these seeming...

متن کامل

Non-Abelian Sequenceable Groups Involving ?-Covers

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

متن کامل

Covering Systems and Their Connections to Zero - Sums

A finite system of residue classes is called a covering system if every integer belongs to one of the residue classes. Paul Erdős invented this concept and initiated the study of this fascinating topic. On the basis of known connections between covering systems and unit fractions, the speaker recently found that covering systems are closely related to zerosum problems on abelian groups (another...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009