Davenport constant with weights and some related questions, II |
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Authors: | Sukumar Das Adhikari |
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Institution: | a Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India b Department of Mathematics, Nanjing Normal University, Nanjing 210097, PR China |
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Abstract: | Let G be a finite abelian group of order n and let A⊆Z be non-empty. Generalizing a well-known constant, we define the Davenport constant of G with weight A, denoted by DA(G), to be the least natural number k such that for any sequence (x1,…,xk) with xi∈G, there exists a non-empty subsequence (xj1,…,xjl) and a1,…,al∈A such that . Similarly, for any such set A, EA(G) is defined to be the least t∈N such that for all sequences (x1,…,xt) with xi∈G, there exist indices j1,…,jn∈N,1?j1<?<jn?t, and ?1,…,?n∈A with . In the present paper, we establish a relation between the constants DA(G) and EA(G) under certain conditions. Our definitions are compatible with the previous generalizations for the particular group G=Z/nZ and the relation we establish had been conjectured in that particular case. |
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Keywords: | Zero-sum problems Davenport constant The EGZ theorem |
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