On the existence of integer relative Heffter arrays
نویسندگان
چکیده
منابع مشابه
Square integer Heffter arrays with empty cells
A Heffter array H(m,n; s, t) is an m× n matrix with nonzero entries from Z2ms+1 such that i) each row contains s filled cells and each column contains t filled cells, ii) every row and column sum to 0, and iii) no element from {x,−x} appears twice. Heffter arrays are useful in embedding the complete graph K2nm+1 on an orientable surface where the embedding has the property that each edge border...
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A Heffter array is an m× n matrix with nonzero entries from Z2mn+1 such that i) every row and column sum to 0, and ii) exactly one of each pair {x,−x} of nonzero elements appears in the array. We construct some Heffter arrays. These arrays are used to build current graphs used in topological graph theory. In turn, the current graphs are used to embed the complete graph K2mn+1 so that the faces ...
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A nested orthogonal array is an OA(N, k, s, g)which contains an OA(M, k, r, g) as a subarray. Here r < s andM<N . Necessary conditions for the existence of such arrays are obtained in the form of upper bounds on k, given N,M, s, r and g. Examples are given to show that these bounds are quite powerful in proving nonexistence. The link with incomplete orthogonal arrays is also indicated. © 2007 E...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2020.112088