Results 31 to 40 of about 488 (79)

Some Determinants Involving Incomplete Fubini Numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
We study some properties of restricted and associated Fubini numbers. In particular, they have the natural extensions of the original Fubini numbers in the sense of determinants.
Komatsu Takao, Ramírez José L.
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On Doubled and Quadrupled Fibonacci Type Sequences

Annales Mathematicae Silesianae
In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled ...
Yilmaz Nur Şeyma, Włoch Andrzej, Özkan Engin, Strzałka Dominik   +3 more
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Square Roots of Real 3 × 3 Matrices vs. Quartic Polynomials with Real Zeros

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
There is an interesting analogy between the description of the real square roots of 3×3 matrices and the zeros of the (depressed) real quartic polynomials.
Anghel Nicolae
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On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers

Annales Mathematicae Silesianae
In this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of
Piejko Krzysztof, Trojnar-Spelina Lucyna
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Determinant Identities and the Geometry of Lines and Circles

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014
The focus of this note is the nontrivial determinant identities which typically underlie the complex analytic proofs of all the results in the plane geometry of lines and circles.
Anghel Nicolae
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The number of rational points of some classes of algebraic varieties over finite fields

Open Mathematics
Let Fq{{\mathbb{F}}}_{q} be the finite field of characteristic pp and Fq*=Fq\{0}{{\mathbb{F}}}_{q}^{* }\left={{\mathbb{F}}}_{q}\backslash \left\{0\right\}.
Zhu Guangyan, Fang Yingjue, Luo Yuanyuan, Lin Zongbing   +3 more
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Determinants of Toeplitz–Hessenberg Matrices with Generalized Leonardo Number Entries

Annales Mathematicae Silesianae
Let un = un(k) denote the generalized Leonardo number defined recursively by un = un−1 + un−2 + k for n ≥ 2, where u0 = u1 = 1. Terms of the sequence un(1) are referred to simply as Leonardo numbers.
Goy Taras, Shattuck Mark
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On the bounded generation of arithmetic ${\rm SL}_2$

, 2019
Let $K$ be a number field and ${\mathcal O}$ be the ring of $S$-integers in $K$. Morgan, Rapinchuck, and Sury have proved that if the group of units ${\mathcal O}^{\times}$ is infinite, then every matrix in ${\rm SL}_2({\mathcal O})$ is a product of at ...
Jordan, Bruce W., Zaytman, Yevgeny
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On the elementary symmetric functions of a sum of matrices

, 2009
Often in mathematics it is useful to summarize a multivariate phenomenon with a single number and in fact, the determinant -- which is represented by det -- is one of the simplest cases.
Costas-Santos, R. S.
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On some determinants involving the tangent function

, 2019
Let $p$ be an odd prime and let $a,b\in\mathbb Z$ with $p\nmid ab$. In this paper we mainly evaluate $$T_p^{(\delta)}(a,b):=\det\left[\tan\pi\frac{aj^2+bk^2}p\right]_{\delta\le j,k\le (p-1)/2}\ \ (\delta=0,1).$$ For example, in the case $p\equiv3\pmod4 ...
Sun, Zhi-Wei
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