Algebraic Geometry

2020


Saniga, M. and Szabó, Zs.: 2020, Magic Three-Qubit Veldkamp Line and Veldkamp Space of the Doily, Symmetry, Vol. 12, No. 6, 963 (8 pages).
[Also http://hal.archives-ouvertes.fr/hal-02136248/en/ and http://arXiv.org/abs/1905.08863].



Bartnicka, E., and Saniga, M.: 2020, Affine and Projective Planes Linked with Projective Lines over Certain Rings of Lower Triangular Matrices, Linear Algebra and its Applications, Vol. 586, No. 1, pp. 377-409.
[Also http://arXiv.org/abs/1903.04287].

2019


Saniga, M., and Bartnicka, E..: 2019, Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules, Axioms, Vol. 8, No. 1, 28 (5 pages).
[Also https://arXiv.org/abs/1812.01916].



Saniga, M., Boulmier, J., Pinard, M., and Holweck, F.: 2019, Veldkamp Spaces of Low-Dimensional Ternary Segre Varieties, Results in Mathematics, Vol. 74, 54 (30 pages).
[Also https://arXiv.org/abs/1806.08965].

2017


Green, R. M., and Saniga, M.: 2017, A Classification of the Veldkamp Lines of the Near Hexagon L_3 times GQ(2, 2), Ars Mathematica Contemporanea, Vol. 12, No. 2, pp. 287-299.
[Also http://hal.archives-ouvertes.fr/hal-00871875/en/ and http://arXiv.org/abs/1310.2897].

2016


Saniga, M.: 2016, Combinatorial Intricacies of Labeled Fano Planes, Entropy, Vol. 18, No. 9, Art. No. 312.
[Also http://hal.archives-ouvertes.fr/hal-01202372/ and http://arXiv.org/abs/1509.06009].

2015


Saniga, M., Holweck, F., and Pracna, P.: 2015, From Cayley-Dickson Algebras to Combinatorial Grassmannians, MDPI Mathematics, Vol. 3, No. 4, pp. 1192-1221.
[Also http://hal.archives-ouvertes.fr/hal-00997125/ and http://arXiv.org/abs/1405.6888].



Saniga, M.: 2015, The Complement of Binary Klein Quadric as a Combinatorial Grassmannian, MDPI Mathematics, Vol. 3, No. 2, pp. 481-486.
[Also http://hal.archives-ouvertes.fr/hal-01064747/ and http://arXiv.org/abs/1409.5691].



Saniga, M., Havlicek, H., Holweck, F., Planat, M., and Pracna, P.: 2015, Veldkamp-Space Aspects of a Sequence of Nested Binary Segre Varieties, Annales de l'Institut Henri Poincaré D, Vol. 2, No. 3, pp. 309-333.
[Also http://hal.archives-ouvertes.fr/hal-00966480/en/ and http://arXiv.org/abs/1403.6714].



Saniga, M.: 2015, A Polygonal Structure of Geometric Hyperplanes of the Split Cayley Hexagon of Order Two, an invited talk given at the brainstorming workshop on Finite-Geometrical Aspects of Quantum Theory, Vienna (Austria), February 23-27, 2015.

2014


Saniga, M.: 2014, From Real Cayley-Dickson Algebras to Combinatorial Grassmannians, a seminar talk given at the Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna (Austria), November 19, 2014.



Saniga, M.: 2014, From Real Cayley-Dickson Algebras to Combinatorial Grassmannians, an invited talk given at the workshop on Current Mathematical Methods of Quantum Information, Belfort (France), September 25, 2014.


2013


Havlicek, H., Odehnal, B., and Saniga, M.: 2013, A Note on Segre Varieties in Characteristic Two, a contributed talk presented at the Workshop and Summer School on Finite Semifields, Padova (Italy), September 13, 2013.



Havlicek, H., Odehnal, B., and Saniga, M.: 2013, A Note on Segre Varieties in Characteristic Two, a contributed talk presented at the 11-th International Conference on Geometry and Applications, Varna (Bulgaria), September 4, 2013.



Saniga, M.: 2013, Twenty-Eight GQ(2,2)s of PG(3,2) and Conwell Heptads of PG(5,2), a brainstorming-session-talk given at the Mathematical Research Institute of Oberwolfach, Oberwolfach (Germany), on March 5, 2013.



Saniga, M.: 2013, GQ(2,4) as a Geometry Derived from the Split Cayley Hexagon of Order Two and the Symplectic Generalized Quadrangle W(3), a brainstorming-session-talk given at the Mathematical Research Institute of Oberwolfach, Oberwolfach (Germany), on February 28, 2013.



Saniga, M.: 2013, Geometric Hyperplanes of the Dual of the Split Cayley Hexagon of Order Two, a brainstorming-session-talk given at the Mathematical Research Institute of Oberwolfach, Oberwolfach (Germany), on February 27, 2013.



Saniga, M.: 2013, Geometric Hyperplanes of the Smallest Split Cayley Hexagon Whose Complements are Bipartite, a brainstorming-session-talk given at the Mathematical Research Institute of Oberwolfach, Oberwolfach (Germany), on February 25, 2013.



Green, R. M., and Saniga, M.: 2013, The Veldkamp Space of the Smallest Slim Dense Near Hexagon, International Journal of Geometric Methods in Modern Physics, Vol. 10, No. 2, 1250082 (15 pages).
[Also http://hal.archives-ouvertes.fr/hal-00409346/en/ and http://arXiv.org/abs/0908.0989].


2012


Blunck, A., Lévay, P., Saniga, M., and Vrana, P.: 2012, Invertible Symmetric 3 x 3 Binary Matrices and GQ(2,4), Linear and Multilinear Algebra, Vol. 60, No. 10, pp. 1143-1154.
[Also http://hal.archives-ouvertes.fr/hal-00512669/en/ and http://arXiv.org/abs/1009.1768].



Havlicek, H., Odehnal, B., and Saniga, M.: 2012, On Invariant Notions of Segre Varieties in Binary Projective Spaces, Designs, Codes and Cryptography, Vol. 62, No. 3, pp. 343-356.
[Also http://hal.archives-ouvertes.fr/hal-00494384/en/ and http://arXiv.org/abs/1006.4492].

2011


Hall, J. L., and Saniga, M.: 2011, Free Cyclic Submodules and Non-Unimodular Vectors, submitted.
[Also http://hal.archives-ouvertes.fr/hal-00608865/en/ and http://arXiv.org/abs/1107.3050].



Saniga, M.: 2011, Projective Lines over Finite Rings, an invited talk given at the Department of Physics and Engineering, Elizabethtown College, Elizabethtown, Pennsylvania (U. S. A.), on May 11, 2011.



Saniga, M.: 2011, The Veldkamp Space of Some Distinguished Finite Geometries, an invited talk presented at the Rocky Mountain Algebraic Combinatorics Seminar, Department of Mathematics, Colorado State University, Fort Collins, Colorado (U. S. A.), on April 29, 2011.



Saniga, M.: 2011, Projective Lines over Finite Rings, an invited Kempner colloquium given at the Department of Mathematics, University of Colorado, Boulder, Colorado (U. S. A.), on April 28, 2011.



Saniga, M.: 2011, Geometric Hyperplanes: Desargues Encodes Doily, to be submitted.
[Also http://hal.archives-ouvertes.fr/hal-00550447/en/ and http://arXiv.org/abs/1101.0977].



Saniga, M.: 2011, On the Veldkamp Space of GQ(4, 2), International Journal of Geometric Methods in Modern Physics, Vol. 8, No. 1, pp. 39-47.
[Also http://hal.archives-ouvertes.fr/hal-00443909/en/ and http://arXiv.org/abs/1001.0659].


2010


Saniga, M.: 2010, Rudiments of Space Cremona Transformations, a seminar talk presented at an intensive mini-workshop on Going Beyond Metric: Black Holes, Non-Locality and Cognition, Tatranská Lomnica (Slovak Republic), October 3-7, 2010.



Saniga, M.: 2010, Snarks: A Brief Overview, a seminar talk presented at an intensive mini-workshop on Going Beyond Metric: Black Holes, Non-Locality and Cognition, Tatranská Lomnica (Slovak Republic), October 3-7, 2010.



Saniga, M., Lévay, P., Planat, M., and Pracna, P.: 2010, Geometric Hyperplanes of the Near Hexagon L_3 times GQ(2, 2), Letters in Mathematical Physics, Vol. 91, No. 1, pp. 93-104.
[Also http://hal.archives-ouvertes.fr/hal-00410681/en/ and http://arXiv.org/abs/0908.3363].



Saniga, M., Green, R. M., Lévay, P., Pracna, P., and Vrana, P.: 2010, The Veldkamp Space of GQ(2,4), International Journal of Geometric Methods in Modern Physics, Vol. 7, No. 7, pp. 1133-1145.
[Also http://hal.archives-ouvertes.fr/hal-00365656/en/ and http://arXiv.org/abs/0903.0715].



2009


Green, R. M., and Saniga, M.: 2009, Near Hexagons and Veldkamp Spaces, a seminar talk presented at the Rocky Mountain Algebraic Combinatorics Seminar, Colorado State University, Fort Collins (U.S.A.), October 16, 2009.



Havlicek, H., and Saniga, M.: 2009, Vectors, Cyclic Submodules and Projective Spaces Linked with Ternions, Journal of Geometry, Vol. 92, Nos. 1-2, pp. 79-90.
[Also http://hal.archives-ouvertes.fr/hal-00288947/en/ and http://arXiv.org/abs/0806.3153].



Planat, M., Minarovjech, M., and Saniga, M.: 2009, Ramanujan Sums Analysis of Long-Period Sequences and 1/f Noise, Europhysics Letters, Vol. 85, 40005 (5 pages).
[Also http://hal.archives-ouvertes.fr/hal-00346442/ and http://arXiv.org/abs/0812.2170].

2008


Saniga, M., and Pracna, P.: 2008, A Jacobson Radical Decomposition of the Fano-Snowflake Configuration, Symmetry, Integrability and Geometry: Methods and Applications, Vol. 4, Paper 072, 7 pages.
[Also http://hal.archives-ouvertes.fr/hal-00295016/ and http://arXiv.org/abs/0807.1790].



Saniga, M., Havlicek, H., Planat, M., and Pracna, P.: 2008, Twin "Fano-Snowflakes" over the Smallest Ring of Ternions, Symmetry, Integrability and Geometry: Methods and Applications, Vol. 4, Paper 050, 7 pages.
[Also http://hal.archives-ouvertes.fr/hal-00268147/en/ and http://arXiv.org/abs/0803.4436].



Saniga, M.: 2008, The (Amazing) Architecture of Finite Projective Ring Lines, a seminar talk presented at the Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna (Austria), March 12, 2008.



Saniga, M., and Planat, M.: 2008, On the Fine Structure of the Projective Line over GF(2) x GF(2) x GF(2), Chaos, Solitons and Fractals, Vol. 37, No. 2, pp. 337-345.
[Also http://hal.ccsd.cnrs.fr/ccsd-00022719 and http://arXiv.org/abs/math.AG/0604307].



Saniga, M., and Planat, M.: 2008, Projective Planes over "Galois" Double Numbers and a Geometrical Principle of Complementarity, Chaos, Solitons and Fractals, Vol. 36, No. 2, pp. 374-381.
[Also http://hal.ccsd.cnrs.fr/ccsd-00016658 and http://arXiv.org/abs/math.NT/0601261].

2007


Saniga, M.: 2007, Projective Ring Lines and Finite Generalized Quadrangles, a review talk presented at the international intensive mini-workshop on Finite Projective Geometries in Quantum Theory, held in Tatranská Lomnica (Slovak Republic), August 1 - 4, 2007.



Saniga, M., Planat, M., Kibler, M. R., and Pracna, P.: 2007, A Classification of the Projective Lines over Small Rings, Chaos, Solitons and Fractals, Vol. 33, No. 4, pp. 1095-1102.
[Also http://hal.ccsd.cnrs.fr/ccsd-00068327 and http://arXiv.org/abs/math.AG/0605301].

2006


Saniga, M., Planat, M., and Pracna, P.: 2006, A Classification of the Projective Lines over Small Rings II. Non-Commutative Case.
[Also http://hal.ccsd.cnrs.fr/ccsd-00080736 and http://arXiv.org/abs/math.AG/0606500].

2000

Saniga, M.: 2000, A Note on a Specific Pencil of Conics in the Galois Fields of Order 2^n, posted at http://arXiv.org/abs/math.AG/0012214.