# 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 F_{3}", *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 q^{2}-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,s^{3})", * J. Alg. Combinatorics*,
Vol. 12, No. 12, pp. 107-113, 2000.

Coolsaet K., "A construction of the simple group of Rudvalis
from the group U_{3}(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,a_{2}=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]