On a class of combinatorial sums involving generalized factorials.
Chou, W.-S., Hsu, L.C., Shiue, P.J.-S. (2007)
International Journal of Mathematics and Mathematical Sciences
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Chou, W.-S., Hsu, L.C., Shiue, P.J.-S. (2007)
International Journal of Mathematics and Mathematical Sciences
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Edoardo Ballico (2010)
Annales UMCS, Mathematica
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Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of S ⊂ X(R) such that P ∈ . Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.
A. Lachlan (1980)
Fundamenta Mathematicae
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A. Lachlan (1974)
Fundamenta Mathematicae
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Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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Zoran Radojičić, Dragan Vukmirović, Nahod Vuković, Miloš Vojinović (2003)
The Yugoslav Journal of Operations Research
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Béla Bajnok, Svetoslav Semov (2014)
Discussiones Mathematicae Probability and Statistics
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We revisit the problem of selecting an item from n choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first k items and then select the first subsequent item that ranks lower than the l-th lowest-ranked item among the first k. We prove that the optimal rule has k ~ n/e, as in the classical secretary problem where our sole objective is to select the item of lowest...
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.
Ali Nesin (1990)
Compositio Mathematica
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Bernard Aupetit, H. Mouton (1996)
Studia Mathematica
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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.
Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.