Mathematics

Silvia Fernandez

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Professor of Mathematics
Email:
Phone:
(818) 677-6445
Office location:
LO 1303F
Website:

Biography

Academic Background

Professor at CSUN since 2001.
Ph.D (Mathematics) Rutgers University, 2001.
B.Sc. (Mathematics) Facultad de Ciencias, UNAM, 1995.

Research

Discrete Geometry, Combinatorics, and Graph Theory.

Publications

B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. The 2-page crossing number of Kn. Discrete and Computational Geometry 49 (2013), no. 4, 747–777.

B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, H. Meijer, V. Sacristán, M. Saumell. Proximity graphs inside large weighted graphs. Networks 61 (2013), 29-39.

B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. The 2-page crossing number of Kn (Extended Abstract). Proceedings of the ACM Symposium on Computational Geometry, June 17–20, 2012, Chapel Hill, North Carolina, USA. (2012) 397-403.

B. M. Ábrego, S. Fernández-Merchant, and G. Salazar. The rectilinear crossing number of Kn: Closing in (or are we?). To appear in Thirty essays in geometric graph theory, J. Pach (Ed), Springer (2012).

B. M. Ábrego, M. Cetina, S. Fernández-Merchant, J. Leaños, and G. Salazar. On (<=k)-edges, crossings, and halving lines of geometric drawings of Kn. Discrete and Computational Geometry 48 (2012), 192-215.

B. M. Ábrego, S. Fernández-Merchant, D. B. Roberts. On the maximum number of isosceles right triangles in a finite point set. Involve 4 (2011), 27-42. DOI 10.2140/involve.2011.4.27

B. M. Ábrego, S. Fernández-Merchant, and B. Llano. An Inequality for Macaulay Functions. Journal of Integer Sequences 14 (2011), Article 11.7.4.

B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, V. Sacristán, M. Saumell. On crossing numbers of geometric proximity graphs. Computational Geometry 44 (2011), 216-233.

B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, J. Leaños, and G. Salazar. There is a unique crossing-minimal rectilinear drawing of K18. Electronic Notes in Discrete Mathematics 38 (2011) 547-552.

B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, H. Meijer, V. Sacristán, M. Saumell. Proximity graphs inside large weighted graphs (extended abstract), Proceedings of the 26th European Workshop on Computational Geometry (EuroCG'10), Dortmund, Germany, March 22-24 (2010) 9-12.

B. M. Ábrego and S. Fernández-Merchant. Point-sets with many similar copies of a pattern: without a fixed number of collinear points or in parallelogram-free position. Geombinatorics 19 (2010), no. 4, 133-145.

B. M. Ábrego and S. Fernández-Merchant. Point-sets in general position with many similar copies of a pattern. Geombinatorics 19 (2010), no. 3, 81-99.

B. M. Ábrego, M. Cetina, S. Fernández-Merchant, J. Leaños, and G. Salazar. 3-symmetric and 3-decomposable drawings of Kn. Discrete Applied Mathematics 158 (2010), no. 12, 1240-1258.

B. M. Ábrego, S. Fernández-Merchant, and B. Llano. On the maximum number of translates in a point set. Discrete and Computational Geometry, 43 (2010), 1-20.

B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, V. Sacristán, M. Saumell. On geometric proximity graphs. Proceedings of XIII Encuentros de Geometría Computacional, Universidad de Zaragoza, Spain, June 29-July 1, (2009) 151-156.

B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with squares. Discrete and Computational Geometry 41 (2009), 77-95.

B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Sum of squares of degrees in a graph. Journal of Inequalities in Pure and Applied Mathematics, 10(3) (2009), Art. 64, 34 pp.

B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. A central approach to bound the number of crossings in a generalized configuration. Electronic Notes in Discrete Mathematics 30 (2008) 273-278.

B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. The maximum number of halving lines and the rectilinear crossing number of Kn for n<=27. Electronic Notes in Discrete Mathematics 30 (2008) 261-266.

B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. An extended lower bound on the number of (<=k)-edges to generalized configurations of points and the pseudolinear crossing number of Kn. Journal of Combinatorial Theory, Series A. 115 (2008), 1257-1264.

B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. Recent developments on the number of (<=k)-sets, halving-lines, and the rectilinear crossing number of Kn. Proceedings of XII Encuentros de Geometría Computacional, Universidad de Valladolid, Spain, June 25-27, (2007), ISBN 978-84-690-6900-4.

B. M. Ábrego and S. Fernández-Merchant. Geometric drawings of Kn with few crossings. Journal of Combinatorial Theory, Series A 114 (2007) 373-379.

B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. On (<=k)–pseudoedges in generalized configurations and the pseudolinear crossing number of Kn. Preprint (2006).

B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Trace-minimal graphs and D-optimal weighing designs, Linear Algebra and its Applications 412 (2006), 161-221.

B. M. Ábrego and S. Fernández-Merchant. A lower bound for the rectilinear crossing number. Graphs and Combinatorics, Springer-Verlag Tokyo Inc., Vol. 21, Num 3, (2005), p. 293 - 300.

B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with geometric objects: combinatorial results. Discrete and Computational Geometry Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004. Springer-Verlag, Lecture Notes in Computer Science Series, Vol. 3742, Akiyama, Jin; Kano, Mikio; Tan, Xuehou (Eds.) 2005, VIII, p. 1-15, ISBN: 3-540-30467-3.

B. M. Ábrego, S. Fernández-Merchant, and Gy. Elekes. Structural results for planar sets with many similar subsets. Combinatorica 24 (2004), no. 4, 541-554.

B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. D-optimal weighing designs for n=-1 (mod 4) objects and a large number of weighings, Linear Algebra and its Applications 374 (2003), 175-218.

B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Maximum volume simplices and trace-minimal graphs, Proceedings of X Encuentros de Geometria Computacional, University of Sevilla, Sevilla Spain, June 16-17, (2003), 51-56.

B. M. Ábrego and S. Fernández-Merchant. The unit distance problem for centrally symmetric convex polygons. Discrete and computational geometry and graph drawing (Columbia, SC, 2001). Discrete and Computational Geometry 28 (2002), no 4, 467-473.

B. M. Ábrego and S. Fernández-Merchant. Convex Polyhedra in R^3 Spanning W(n^(4/3)) Congruent Triangles, Journal of Combinatorial Theory, Series A 98, 406-409 (2002).

B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles II. DIMACS Technical Report 99-47, (1999).

B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles I. Discrete and Computational Geometry 23, (2000), no. 1, 129-115.

B. M. Ábrego, J. L. Arocha, S. Fernández-Merchant, and V. Neumann-Lara. Tightness Problems in the Plane. Discrete Mathematics 194 (1999), no. 1-3, 1-11.