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The Well-Covered Dimension Of Products Of Graphs

Isaac Birnbaum, Megan Kuneli, Robyn McDonald, Katherine Urabe, Oscar Vega (2014)

Discussiones Mathematicae Graph Theory

We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of Kn × G is found, provided that G has a largest greedy independent decomposition of length c < n. Formulae to find the well-covered dimension of graphs obtained by vertex blowups on a known graph, and to the lexicographic product of two known graphs are also given.

Two point sets with additional properties

Marek Bienias, Szymon Głąb, Robert Rałowski, Szymon Żeberski (2013)

Czechoslovak Mathematical Journal

A subset of the plane is called a two point set if it intersects any line in exactly two points. We give constructions of two point sets possessing some additional properties. Among these properties we consider: being a Hamel base, belonging to some σ -ideal, being (completely) nonmeasurable with respect to different σ -ideals, being a κ -covering. We also give examples of properties that are not satisfied by any two point set: being Luzin, Sierpiński and Bernstein set. We also consider natural generalizations...

Two problems related to the non-vanishing of L ( 1 , χ )

Paolo Codecà, Roberto Dvornicich, Umberto Zannier (1998)

Journal de théorie des nombres de Bordeaux

We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or ( ( x y / q ) ) , ( 0 ≤ x , y &lt; q ) , where ( ( u ) ) = u - [ u ] - 1 / 2 denotes the “centered” fractional part of x . These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet L -functions at s = 1 .

Universal bounds for matrix semigroups

Leo Livshits, Gordon MacDonald, Heydar Radjavi (2011)

Studia Mathematica

We show that any compact semigroup of n × n matrices is similar to a semigroup bounded by √n. We give examples to show that this bound is best possible and consider the effect of the minimal rank of matrices in the semigroup on this bound.

Weak products of universal algebras

Ildikó Sain (1993)

Banach Center Publications

Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.

Zero-term rank preservers of integer matrices

Seok-Zun Song, Young-Bae Jun (2006)

Discussiones Mathematicae - General Algebra and Applications

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.

Zero-term ranks of real matrices and their preservers

LeRoy B. Beasley, Young Bae Jun, Seok-Zun Song (2004)

Czechoslovak Mathematical Journal

Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve zero-term rank of the m × n real matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix.

Currently displaying 181 – 200 of 206