Relevant bibliographies by topics / Equiangular lines

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Equiangular lines'

Author: Grafiati
Published: 18 May 2024

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Journal articles on the topic "Equiangular lines"

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Et-Taoui, Boumediene. "Quaternionic equiangular lines." Advances in Geometry 20, no. 2 (April 28, 2020): 273–84. http://dx.doi.org/10.1515/advgeom-2019-0021.

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AbstractLet 𝔽 = ℝ, ℂ or ℍ. A p-set of equi-isoclinic n-planes with parameter λ in 𝔽r is a set of pn-planes spanning 𝔽r each pair of which has the same non-zero angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. It is known that via a complex matrix representation, a pair of isoclinic n-planes in ℍr with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$ yields a pair of isoclinic 2n-planes in ℂ2r with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. In this article we characterize all the p-tuples of equi-isoclinic planes in ℂ2r which come via our complex representation from p-tuples of equiangular lines in ℍr. We then construct all the p-tuples of equi-isoclinic planes in ℂ4 and derive all the p-tuples of equiangular lines in ℍ2. Among other things it turns out that the quadruples of equiangular lines in ℍ2 are all regular, i.e. their symmetry groups are isomorphic to the symmetric group S4.
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Et-Taoui, B. "Equiangular lines in Cr." Indagationes Mathematicae 11, no. 2 (June 2000): 201–7. http://dx.doi.org/10.1016/s0019-3577(00)89078-3.

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Deza, M., and V. P. Grishukhin. "L-polytopes and equiangular lines." Discrete Applied Mathematics 56, no. 2-3 (January 1995): 181–214. http://dx.doi.org/10.1016/0166-218x(94)00086-s.

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Greaves, Gary, Jacobus H. Koolen, Akihiro Munemasa, and Ferenc Szöllősi. "Equiangular lines in Euclidean spaces." Journal of Combinatorial Theory, Series A 138 (February 2016): 208–35. http://dx.doi.org/10.1016/j.jcta.2015.09.008.

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Deza, M., and V. P. Grishukhin. "Cut Lattices and Equiangular Lines." European Journal of Combinatorics 17, no. 2-3 (February 1996): 143–56. http://dx.doi.org/10.1006/eujc.1996.0013.

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Et-Taoui, B. "Equiangular lines in Cr (part II)." Indagationes Mathematicae 13, no. 4 (2002): 483–86. http://dx.doi.org/10.1016/s0019-3577(02)80027-1.

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Mondal, Bishwarup, Roopsha Samanta, and Robert W. Heath. "Congruent Voronoi tessellations from equiangular lines." Applied and Computational Harmonic Analysis 23, no. 2 (September 2007): 254–58. http://dx.doi.org/10.1016/j.acha.2007.03.005.

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Lin, Yen-Chi Roger, and Wei-Hsuan Yu. "Equiangular lines and the Lemmens–Seidel conjecture." Discrete Mathematics 343, no. 2 (February 2020): 111667. http://dx.doi.org/10.1016/j.disc.2019.111667.

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Balla, Igor, Felix Dräxler, Peter Keevash, and Benny Sudakov. "Equiangular lines and subspaces in Euclidean spaces." Electronic Notes in Discrete Mathematics 61 (August 2017): 85–91. http://dx.doi.org/10.1016/j.endm.2017.06.024.

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Guiduli, B., and M. Rosenfeld. "Ubiquitous Angles in Equiangular Sets of Lines." Discrete & Computational Geometry 24, no. 2 (September 2000): 313–24. http://dx.doi.org/10.1007/s004540010038.

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Dissertations / Theses on the topic "Equiangular lines"

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Lehbab, Imène. "Problèmes métriques dans les espaces de Grassmann." Electronic Thesis or Diss., Mulhouse, 2023. http://www.theses.fr/2023MULH6508.

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Il s'agit d'une contribution dans le domaine de la géométrie métrique du plan projectif complexe CP2 et de la variété de Grassmann réelle des plans dans R6. On s'intéresse à l'étude de tous les p-uplets, p ≥ 3, de droites équiangulaires dans C3 et des p-uplets de plans équi-isoclins dans R6. Sachant que 9 est le nombre maximum de droites équiangulaires que l'on peut construire dans C3, on décrit une méthode qui permet de construire tous les p-uplets de droites équiangulaires pour tout pϵ[3,9]. En particulier, on construit dans C3 cinq classes de congruence de quadruplets de droites équiangulaires dont une dépend d'un paramètre réel ɣ que l'on étend à une famille infinie de sextuplets de droites équiangulaires dépendant du même paramètre réel ɣ. En outre, on donne les angles pour lesquels nos sextuplets s'étendent au-delà et jusqu'aux 9-uplets. On sait qu'il existe un p-uplet, p≥3, de plans équi-isoclins engendrant Rr, r≥4, de paramètre c, 0
This work contributes to the field of metric geometry of the complex projective plane CP2 and the real Grassmannian manifold of the planes in R6. More specifically, we study all p-tuples, p ≥ 3, of equiangular lines in C3 or equidistant points in CP2, and p-tuples of equi-isoclinic planes in R6. Knowing that 9 is the maximum number of equiangular lines that can be constructed in C3, we develop a method to obtain all p-tuples of equiangular lines for all p ϵ [3,9]. In particular, we construct in C3 five congruence classes of quadruples of equiangular lines, one of which depends on a real parameter ɣ, which we extend to an infinite family of sextuples of equiangular lines depending on the same real parameter ɣ. In addition, we give the angles for which our sextuples extend beyond and up to 9-tuples. We know that there exists a p-tuple, p ≥ 3, of equi-isoclinic planes generating Rr, r ≥ 4, with parameter c, 0< c <1, if and only if there exists a square symmetric matrix, called Seidel matrix, of p × p square blocks of order 2, whose diagonal blocks are all zero and the others are orthogonal matrices in O(2) and whose smallest eigenvalue is equal to - 1/c and has multiplicity 2p-r. In this thesis, we investigate the case r=6 and we also show that we can explicitly determine the spectrum of all Seidel matrices of order 2p, p ≥ 3 whose off-diagonal blocks are in {R0, S0} where R0 and S0 are respectively the zero-angle rotation and the zero-angle symmetry. We thus show an unexpected link between some p-tuples of equi-isoclinic planes in Rr and simple graphs of order p
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Mirjalalieh, Shirazi Mirhamed. "Equiangular Lines and Antipodal Covers." Thesis, 2010. http://hdl.handle.net/10012/5493.

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It is not hard to see that the number of equiangular lines in a complex space of dimension $d$ is at most $d^{2}$. A set of $d^{2}$ equiangular lines in a $d$-dimensional complex space is of significant importance in Quantum Computing as it corresponds to a measurement for which its statistics determine completely the quantum state on which the measurement is carried out. The existence of $d^{2}$ equiangular lines in a $d$-dimensional complex space is only known for a few values of $d$, although physicists conjecture that they do exist for any value of $d$. The main results in this thesis are: \begin{enumerate} \item Abelian covers of complete graphs that have certain parameters can be used to construct sets of $d^2$ equiangular lines in $d$-dimen\-sion\-al space; \item we exhibit infinitely many parameter sets that satisfy all the known necessary conditions for the existence of such a cover; and \item we find the decompose of the space into irreducible modules over the Terwilliger algebra of covers of complete graphs. \end{enumerate} A few techniques are known for constructing covers of complete graphs, none of which can be used to construct covers that lead to sets of $d^{2}$ equiangular lines in $d$-dimensional complex spaces. The third main result is developed in the hope of assisting such construction.
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Eubanks, Travis Wayne. "A Compact Parallel-plane Perpendicular-current Feed for a Modified Equiangular Spiral Antenna and Related Circuits." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-7801.

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This work describes the design and measurement of a compact bidirectional ultrawideband (UWB) modified equiangular spiral antenna with an integrated feed internally matched to a 50-Ohm microstrip transmission line. A UWB transition from microstrip to double-sided parallel-strip line (DSPSL) soldered to a short (1.14 mm) twin-line transmission line feeds the spiral. The currents on the feed travel in a direction approximately perpendicular to the direction of the currents on the spiral at the points where the feed passes the spiral in close proximity (0.57 mm). Holes were etched from the metal arms of the spiral to reduce the impedance mismatch caused by coupling between the transmission line feed and the spiral. This work also describes a low-loss back-to-back transition from coaxial line to DSPSL, an in-phase connectorized 3 dB DSPSL power divider made using three of those transitions, a 2:1 in-phase DSPSL power divider, a 3:1 in-phase DSPSL power divider, a radial dipole fed by DSPSL, an array of those dipoles utilizing the various power dividers, and a UWB circular monopole antenna fed by DSPSL. Measured and simulated results show good agreement for the designed antennas and circuits.
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Book chapters on the topic "Equiangular lines"

1

Matoušek, Jiří. "Equiangular lines." In The Student Mathematical Library, 27–29. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/stml/053/09.

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Stacey, Blake C. "Equiangular Lines." In A First Course in the Sporadic SICs, 1–11. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76104-2_1.

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Grassl, Markus. "Computing Equiangular Lines in Complex Space." In Mathematical Methods in Computer Science, 89–104. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-89994-5_8.

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Jedwab, Jonathan, and Amy Wiebe. "A Simple Construction of Complex Equiangular Lines." In Algebraic Design Theory and Hadamard Matrices, 159–69. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17729-8_13.

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LEMMENS, P. W. H., J. J. SEIDEL, and J. A. Green. "Equiangular Lines." In Geometry and Combinatorics, 127–45. Elsevier, 1991. http://dx.doi.org/10.1016/b978-0-12-189420-7.50017-7.

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Journal articles
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