8 citations · 10 across the 10 of their papers we have counts for
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Sign-restricted matrices of 's, 's, and 's
Richard A. Brualdi, Geir Dahl
We study {\em sign-restricted matrices} (SRMs), a class of rectangular -matrices generalizing the alternating sign matrices (ASMs). In an SRM each partial column sum, s…
Convex -Matrices and Their Epitopes
Richard A. Brualdi, Geir Dahl
We investigate -matrices that are {\em convex}, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of…
Diagonal Sums of Doubly Stochastic Matrices
Richard A. Brualdi, Geir Dahl
Let denote the class of doubly stochastic matrices (each such matrix is entrywise nonnegative and every row and column sum is 1). We study the diagonals of matri…
Pattern-Avoiding (0,1)-Matrices
Richard A. Brualdi, Lei Cao
We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain ex…
Permutation Matrices, Their Discrete Derivatives and Extremal Properties
Richard A. Brualdi, Geir Dahl
For a permutation , and the corresponding permutation matrix, we introduce the notion of {\em discrete derivative}, obtained by taking differences of successive entries in .…
Alternating Sign Matrices and Hypermatrices, and a Generalization of Latin Square
Richard A. Brualdi, Geir Dahl
An alternating sign matrix, or ASM, is a -matrix where the nonzero entries in each row and column alternate in sign. We generalize this notion to hypermatrices: an $n\t…