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Which young tableaux can represent an outer sum?

Author(s): Mallows, C; Vanderbei, Robert J.

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dc.contributor.authorMallows, C-
dc.contributor.authorVanderbei, Robert J.-
dc.date.accessioned2016-10-17T14:14:52Z-
dc.date.available2016-10-17T14:14:52Z-
dc.date.issued2015-07-30en_US
dc.identifier.citationMallows, C, Vanderbei, RJ. "Which young tableaux can represent an outer sum?" Journal of Integer Sequences, 18(9), 2015.en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr14p4b-
dc.description.abstract© 2015, University of Waterloo. All rights reserved.Given two vectors, not necessarily of the same length, each having increasing elements, we form the matrix whose (i, j)-th element is the sum of the i-th element from the first vector and the j-th element from the second vector. Such a matrix is called an outer sum of the two vectors (a concept that is analogous to outer products). If we assume that all the entries of this matrix are distinct, then we can form another matrix of the same size but for which the (i, j)-th element is not the matrix element itself but rather the rank of this element in a sorted list of all the numbers in the first matrix. Such a matrix is called a Young tableau. We say that it "represents" the outer sum. In this paper, we address the question as to whether all Young tableaux can be generated this way. When one of the two dimensions is two, then the answer is yes. In all higher dimensional cases, the answer is no. We prove the positive result and give examples illustrating the negative result.en_US
dc.relation.ispartofJournal of Integer Sequencesen_US
dc.rightsThis is the author’s final manuscript. All rights reserved to author(s).en_US
dc.titleWhich young tableaux can represent an outer sum?en_US
dc.typeJournal Articleen_US
dc.identifier.eissn1530-7638-

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