Inverse problems associated with subsequence sums in \(C_p \oplus C_p\). (English) Zbl 1461.11134
Summary: Let \(G\) be a finite abelian group and \(S\) be a sequence with elements of \(G\). We say that \(S\) is a regular sequence over \(G\) if \(\mid S_H \mid \leqslant \mid H \mid - 1\) holds for every proper subgroup \(H\) of \(G\), where \(S_H\) denotes the subsequence of \(S\) consisting of all terms of \(S\) contained in \(H\). We say that \(S\) is a zero-sum free sequence over \(G\) if \(0 \not\in \Sigma (S)\), where \(\Sigma (S) \subset G\) denotes the set of group elements which can be expressed as a sum of a nonempty subsequence of \(S\). In this paper, we study the inverse problems associated with \(\Omega (S)\) when \(S\) is a regular sequence or a zero-sum free sequence over \(G = C_p \oplus C_p\), where \(p\) is a prime.
MSC:
| 11P70 | Inverse problems of additive number theory, including sumsets |
| 11B13 | Additive bases, including sumsets |
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