The rank of a cograph.
Royle, Gordon F. (2003)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “On the function “sandwiched' between and .”
The rank of a cograph.
Minimum rank of a tree over an arbitrary field.
Chenette, Nathan L., Droms, Sean V., Hogben, Leslie, Mikkelson, Rana, Pryporova, Olga (2007)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Low rank co-diagonal matrices and Ramsey graphs.
Grolmusz, Vince (2000)
The Electronic Journal of Combinatorics [electronic only]
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On the functions with values in .
Dobrynin, V., Pliskin, M., Prosolupov, E. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Universally optimal matrices and field independence of the minimum rank of a graph.
Dealba, Luz M., Grout, Jason, Hogben, Leslie, Mikkelson, Rana, Rasmussen, Kaela (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.
Berman, Avi, Friedland, Shmuel, Hogben, Leslie, Rothblum, Uriel G., Shader, Bryan (2008)
The Electronic Journal of Combinatorics [electronic only]
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More counterexamples to the Alon-Saks-Seymour and rank-coloring conjectures.
Cioabă, Sebastian M., Tait, Michael (2011)
The Electronic Journal of Combinatorics [electronic only]
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Minimal rank.
Shaked-Monderer, Naomi (2001)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Possible numbers ofx’s in an {x,y}-matrix with a given rank
Chao Ma (2017)
Open Mathematics
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Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
Trivial Selmer groups and even partitions of a graph.
Brown, Morgan V., Calkin, Neil J., James, Kevin, King, Adam J., Lockard, Shannon, Rhoades, Robert C. (2006)
Integers
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A basic decomposition result related to the notion of the rank of a matrix and applications.
Mortici, Cristinel (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Zero-term rank preservers of integer matrices
Seok-Zun Song, Young-Bae Jun (2006)
Discussiones Mathematicae - General Algebra and Applications
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The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.
The maximal and minimal ranks of with applications.
Tian, Yongge, Cheng, Shizhen (2003)
The New York Journal of Mathematics [electronic only]
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Linear maps preserving rank 2 on the space of alternate matrices and their applications.
Cao, Chongguang, Tang, Xiaomin (2004)
International Journal of Mathematics and Mathematical Sciences
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