Publications (in preparation)

[ Some preprints are available here.]

Publications

Coolsaet K., "Spherical quadrangles with three equal sides and rational angles", Ars Mathematicae Contemporanea, Vol 12(2), 415-424, 2017.

Schein S., Yeh A, Coolsaet K. and Gayed J., "Decoration of the Truncated Tetrahedron—An Archimedean Polyhedron—To Produce a New Class of Convex Equilateral Polyhedra with Tetrahedral Symmetry", Symmetry, Vol 8(8), 82, 2016.

Coolsaet K., "The complete arcs of PG(2,31)", Journal of Combinatorial Designs, Vol 23(12), 522-533, 2015.

Coolsaet K., Sticker H., "Arcs with large conical subsets in Desarguesian planes of even order", Electronic Journal of Combinatorics, Vol 21(1), P1.14, 2014.

Coolsaet K., "Some large partial ovoids of Q-(5,q), for q odd", Designs, Codes and Cryptography - Vol 72(1), pp. 119-128, 2014.

Coolsaet K., "On the classification of nonsingular 2×2×2×2 hypercubes", Designs, Codes and Cryptography, Vol 68(1-3), pp. 179-194, 2013.

Coolsaet K., "Fast vector arithmetic over F3", Bulletin of the Belgian Mathematical Society, Vol 20, pp. 329-344, 2013.

Coolsaet K., J. De Beule, A. Siciliano, "The known maximal partial ovoids of size q2-1 of Q(4,q)", Journal of Combinatorial Designs, Vol 21(3), pp. 89-100, 2013.

Brinkmann G., Goedgebeur J., Mélot H., Coolsaet K., "House of Graphs: a database of interesting graphs", Discrete Applied Mathematics, Vol 161, pp. 311-314, 2013.

Coolsaet K., P.D. Johnson, Jr., K. J. Roblee, T. D. Smotzer, "Some extremal problems for edge-regular graphs", Ars Combinatoria, Vol 105, pp. 411-418, 2012.

Coolsaet K., Sticker H., "The complete (k,3)-arcs of PG(2,q), q ≤ 13", Journal of Combinatorial Designs, Vol 20(2), pp. 89-111, 2012.

Coolsaet K., "The Lemma of Tangents reformulated", Discrete Mathematics, Vol 312, pp. 705-714, 2012.

Coolsaet K., Sticker H., "The complete k-arcs of PG(2,27) and PG(2,29)", Journal of Combinatorial Designs, Vol 19(2), pp. 111-130, 2011.

Coolsaet K., "The smallest split Cayley hexagon has two symplectic embeddings", Finite Fields and their Applications, Vol 16(5), pp. 380-384, 2010.

Coolsaet K., Sticker H., "Arcs with Large Conical Subsets", Electronic Journal of Combinatorics, Vol 17(1), R112, 2010.

Coolsaet K., Sticker H., "A full classification of the complete k-arcs of PG(2,23) and PG(2,25)", Journal of Combinatorial Designs, Vol 17(6), pp. 459-477, 2009.

Peeters A., Coolsaet K., Brinkmann G., Van Cleemput N., Fack V., "GrInvIn in a Nutshell", Journal of Mathematical Chemistry, Vol 45(2), pp. 471-477, 2009.

Coolsaet K., Jurišić A., "Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs", Journal of Combinatorial Theory, Series A, Vol 115, pp. 1086-1095, 2008.

Coolsaet K., Jurišić A., Koolen J., "On triangle-free distance-regular graphs with an eigenvalue multiplicity equal to the valency", European Journal of Combinatorics, Vol 29(5), pp. 1186-1199, 2008.

Coolsaet K., Degraer J., "Using algebraic properties of minimal idempotents for exhaustive computer generation of association schemes", Electronic Journal of Combinatorics, Vol 15(1), R30, 2008.

Degraer J., Coolsaet K., "Classification of some strongly regular subgraphs of the McLaughlin graph", Discrete Mathematics, Vol 308, pp. 395-400, 2008.

Coolsaet K., "A 51-dimensional embedding of the Ree-Tits generalized octagon", Designs, Codes and Cryptography, Vol 47 (1-3), pp. 75-97, 2008.

Coolsaet K., "On a 25-dimensional embedding of the Ree-Tits generalized octagon", Advances in Geometry, Vol 7, No. 3, pp. 423-452, 2007.

Coolsaet K., J. Degraer, E. Spence, "The Strongly Regular (45,12,3,3) graphs", Electronic Journal of Combinatorics, Vol 13(1), R32, 2006.

Coolsaet K., "The uniqueness of the strongly regular graph srg(105,32,4,12)", Bulletin of the Belgian Mathematical Society - Simon Stevin, Vol 12, No. 5, pp. 707-718, 2005.

Degraer J., Coolsaet K., "Classification of three-class association schemes using backtracking with dynamic variable ordering", Discrete Mathematics, Vol 300, No. 1-3, pp. 71-81, 2005.

Coolsaet K., Degraer J., "A computer assisted proof of the uniqueness of the Perkel graph", Designs, Codes and Cryptography, Vol 34, No.2-3, pp. 155-171, 2005.

Coolsaet K., "Algebraic structure of the perfect Ree-Tits generalized octagons", Innovations in Incidence Geometry, Vol 1, pp. 67-131, 2005. [NON-ISI]

Coolsaet K., "A distance regular graph with intersection array (21,16,8;1,4,14) does not exist", European Journal of Combinatorics, Vol 26, No. 5, pp. 709-716, 2005.

Coolsaet K., "Some combinatorial properties of finite generalized octagons", Proceedings of the Academy Contact Forum on Generalized Polygons (Ed. F. De Clerck, L. Storme, J.A. Thas, H. Van Maldeghem), Koninklijke Vlaamse Academie van België, pp. 23-38, 2000. [CONF-PROC]

Coolsaet K., Van Maldeghem H., "Some new upper bounds for the size of partial ovoids in slim generalized polygons and generalized hexagons of order (s,s3)", J. Alg. Combinatorics, Vol. 12, No. 12, pp. 107-113, 2000.

Coolsaet K., "A construction of the simple group of Rudvalis from the group U3(5):2", J. Group Theory, Vol. 1, No. 2, pp. 143-163, 1998.

Batten L.M., K. Coolsaet & A.P. Street, "Blocking sets in (v, {2,4}, 1)-Designs", Designs, Codes and Cryptography, Vol. 10, No. 3, pp. 309-314, 1997. [NON-ISI]

Coolsaet K., "Local structure of graphs with lambda=mu=2,a2=4.", Combinatorica, Vol. 15 (04), pp. 481-488, 1995.

Fack V., K. Coolsaet, & H. De Meyer, "Using a tabular method for verification of total exchange algorithms on networks of parallel processors", Parallel Computing: Trends and Applications, Proceedings of the International Conference ParCo93 (Ed. G.R. Joubert, D. Trystram, F.J. Peters, D.J. Evans), North Holland, 1994, pp. 605-608. [CONF-PROC]

Coolsaet K., Fack V. & Demeyer H., "A tabular method for verification of data exchange algorithms on networks of parallel processors", Nordic Journ. of Comp., Vol. 1, pp. 202-213, 1994. [NON-ISI]

Coolsaet K. & Fack V., "Optimal Data Exchange Algorithms on Star Graphs", Computers Math. Applic., Vol. 27, No. 3, pp. 21-25, 1994.

Coolsaet K., "A quick introduction to the programming language MIKE", SIGPLAN Notices, Vol. 27, No. 3, pp. 37-46, 1992.

Coolsaet K., H. Demeyer & V. Fack,"Optimal Algorithms for Total Exchange without Buffering on the Hypercube", BIT, Vol 32 pp. 559-569, 1992.

Coolsaet K. & V. Fack, "Classifying strongly regular graphs using lexical ordering of adjacency matrices", Computers Math. Applic., Vol. 21, No. 2-3, pp. 15-21, 1991.

Coolsaet K. & V. Fack, "Total Exchange Algorithms on 'sandwich graphs'", Computers Math. Applic., Vol. 22, No. 10, pp. 45-48, 1991.

Fack V. & K. Coolsaet, "An algorithm for the classification of strongly regular graphs by means of lexically ordered adjacency matrices", Intern. J. Computer Math., Vol. 33, pp. 143-151, 1990.

Coolsaet K. & Cz. Bylinski, "MIZAR MSE on the MAID-machine", Computerized Logic Teaching Bulletin, Association of Computerized Logic Teaching, Vol. 1, No. 2, 1988. [NON-ISI]

Coolsaet K., "An introduction to MIKE, a new structured programming language", Studies in Logic, Grammar and Rhetoric VII, BIALYSTOCK 1988. [NON-ISI]

Coolsaet K., "IF-THEN-ELSE calculus applied to propositional logic", MIZAR News, STOCKHOLM, 1987.[NON-ISI]

Coolsaet K., "IF-THEN-ELSE calculus applied to propositional logic", Studies in Logic, Grammar and Rhetoric VI, BIALYSTOCK 1987 [NON-ISI]

Coolsaet K. & A. Hoogewijs, "A formal system for proof checking in MIZAR", Studies in Logic, Grammar and Rhetoric V, BIALYSTOCK 1986 [NON-ISI]