Search

Given A ⊆ Zn, the A-weighted zero-sum constant CA is defined to be the smallest natural number k such that any sequence of k elements in Zn has an A-weighted zero-sum subsequence of consecutive terms. A sequence of length CA - 1 in Zn which does not have any A-weighted zero-sum subsequence of consecutive terms is called a C-extremal sequence for A. For n odd, let S(n) be the set of all units in Zn whose Jacobi symbol with respect to n is one. Given a prime divisor p of n, let L(n; p) be the set of all units Zn whose Jacobi symbol with respect to n is the same as their Legendre symbol with respect to p. We characterize the C-extremal sequences for S(n) and L(n; p). Given A = Zn, the A-weighted Davenport constant DA is defined to be the smallest natural number k such that any sequence of k elements in Zn has an A-weighted zero-sum subsequence. A sequence of length DA - 1 in Zn which does not have any A-weighted zero-sum subsequence is called a D-extremal sequence for A. We characterize the D-extremal sequences for S(n) and L(n; p). [ABSTRACT FROM AUTHOR]