Classification theorems for sumsets modulo a prime

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Nguyen, Hoi
Vu, Van
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Let $\Z/pZ$ be the finite field of prime order $p$ and $A$ be a subsequence of $\Z/pZ$. We prove several classification results about the following questions: (1) When can one represent zero as a sum of some elements of $A$ ? (2) When can one represent every element of $\Z/pZ$ as a sum of some elements of $A$ ? (3) When can one represent every element of $\Z/pZ$ as a sum of $l$ elements of $A$ ?
Comment: 35 pages, to appear in JCT A
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Mathematics - Combinatorics
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