Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900523 | Advances in Applied Mathematics | 2018 | 36 Pages |
Abstract
An alternating sign matrix, or ASM, is a (0,±1)-matrix where the nonzero entries in each row and column alternate in sign. We generalize this notion to hypermatrices: an nÃnÃn hypermatrix A=[aijk] is an alternating sign hypermatrix, or ASHM, if each of its planes, obtained by fixing one of the three indices, is an ASM. Several results concerning ASHMs are shown, such as finding the maximum number of nonzeros of an nÃnÃn ASHM, and properties related to Latin squares. Moreover, we investigate completion problems, in which one asks if a subhypermatrix can be completed (extended) into an ASHM. We show several theorems of this type.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Richard A. Brualdi, Geir Dahl,