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20 papers · 1 filter
Patterns of Alternating Sign Matrices
Richard A. Brualdi, Kathleen P. Kiernan, Seth A. Meyer +1
We initiate a study of the zero-nonzero patterns of n by n alternating sign matrices. We characterize the row (column) sum vectors of these patterns and determine their minimum ter…
On the t-Term Rank of a Matrix
Richard A. Brualdi, Kathleen P. Kiernan, Seth A. Meyer +1
For t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest number of 1s in A with at most one 1 in each column and at most t 1s in each row. Thus th…
Zero Forcing Sets and Bipartite Circulants
Seth A. Meyer
In this paper we introduce a class of regular bipartite graphs whose biadjacency matrices are circulant matrices and we describe some of their properties. Notably, we compute upper…
Tridiagonal matrices with nonnegative entries
Kazumasa Nomura, Paul Terwilliger
In this paper we characterize the nonnegative irreducible tridiagonal matrices and their permutations, using certain entries in their primitive idempotents. Our main result is summ…
Flexagons yield a curious Catalan number identity
David Callan
Hexaflexagons were popularized by the late Martin Gardner in his first Scientific American column in 1956. Oakley and Wisner showed that they can be represented abstractly by certa…
Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes
Hajime Tanaka, Rie Tanaka
Suzuki (1998) showed that an imprimitive Q-polynomial association scheme with first multiplicity at least three is either Q-bipartite, Q-antipodal, or with four or six classes. The…