Tony Forbes
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E-mail me at anthony.d.forbes[at-sign]gmail.com for items not available online.
Zoe's Design: A poster for Peter Cameron's 60th birthday, Ambleside, August 2007.
See also Theorem of the Day, Number 100.
Geometric Graph Designs: Slides for BCC 2011 talk, Exeter, July 2011.
Applications of Weil's Theorem on Character Sums: Notes for a talk given at London South Bank University, 7 September 2007.
Configurations and colouring problems in block designs, Ph.D.
thesis, The Open University, November 2006.
⇒ Abstract.
⇒ The Thesis. Please e-mail me to say so if you download it. - Thanks.
Steiner triple system configuration data: 6 blocks : 7 blocks : 8 blocks : 9 blocks : Tradeable : Dense.
A collection of small triple systems.
[with T. S. Griggs and K. A. Forbes], Completing the design spectra for graphs with six vertices and eight edges, Australas. J. Combin. 70 (2018), 386-389.
[with T. S. Griggs], Designs for graphs with six vertices and nine edges, Australas. J. Combin. 70 (2018), 52-74 .
[with T. S. Griggs and T. J. Forbes], Theta Graph Designs, J. Algorithms and Computation 49 issue 1 (2017) 1-16; http://arxiv.org/abs/1703.01483.
[with T. S. Griggs and T. J. Forbes], Archimedean graph designs - II, Discrete Math. 340 (2017) 1598-1611.
Designs for 24-vertex snarks, Utilitas Math., accepted, 2016; http://arxiv.org/abs/1607.04847.
[with T. J. Forbes], Hanoi revisited, Math. Gazette 100 (November 2016), 435-441.
Snark designs, Utilitas Math., accepted, 2015; https://arxiv.org/abs/1207.3032v2
[with T. S. Griggs, C. Psomas and J. Širáň]. Biembeddings of Steiner triple systems in orientable pseudosurfaces with one pinch point, Glasgow Mathematical Journal, 56 (2), (May 2014), 251-260.
[with T. S. Griggs], Icosahedron designs, Australas. J. Combin., 52 (2012), 215-228.
[with T. S. Griggs], Archimedean graph designs, Discrete Math., 313 (2013) 1138-1149.
[with P. Adams, D. E. Bryant and T. S. Griggs], Decomposing the complete graph into dodecahedra, J. Statistical Planning and Inference 142 (2012), 1040-1046.
[with T. S. Griggs and F. C. Holroyd], Truncated Tetrahedron, Octahedron and Cube Designs, J. Combinatorial Mathematics and Combinatorial Computing, 80 (2012), 95-111.
[with C. J. Colbourn, M. J. Grannell, T. S. Griggs, P. Kaski, P. R. J. Östergård, D. A. Pike, and O. Pottonen], Properties of the Steiner Triple Systems of Order 19,
Electronic Journal of Combinatorics, 17(1), 2010, R98, 30pp.
Eleven Billion STS(19)s: Slides for talks given at PCC, Warwick, June 2009, and at LSBU, September 2009.
[with T. S. Griggs and F.C. Holroyd], Rhombicuboctahedron designs, J. Combinatorial Mathematics and Combinatorial Computing, 75 (2010), 161-165.
[with M. J. Grannell and T. S. Griggs], Further 6-sparse Steiner triple systems, Graphs and Combinatorics 25 (2009), 49-64.
[with M. J. Grannell, T. S. Griggs and R. G. Stanton], On the small covering numbers g1(5)(v), Utilitas Mathematica 74 (2007), 77-96.
[with M. J. Grannell and T. S. Griggs], New type-B colorable S(2,4,v) designs, J. Combin. Designs 15 (2007), 357-368.
[with M. J. Grannell and T. S. Griggs], The Design of the Century,
Mathematica Slovaca 57 (2007) No. 5, 495-499.
See also Theorem of the Day, Number 100.
[with M. J. Grannell and T. S. Griggs], On 6-sparse Steiner triple systems, J. Combin. Theory, Series A 114 (2007), 235-252.
[with M. J. Grannell and T. S. Griggs], Distance and fractional isomorphism in Steiner triple systems, Rendiconti del Circolo Matematico di Palermo, Series II LVI (2007), 17-32.
[with M. J. Grannell and T. S. Griggs], Steiner triple systems and existentially closed graphs, Electronic Journal of Combinatorics 12 (2005), #R42.
[with M. J. Grannell and T. S. Griggs], On independent sets, Mathematica Slovaca 55 No. 4 (2005), 375-377.
[with M. J. Grannell and T. S. Griggs], Independent sets in Steiner triple systems, Ars Combinatoria 72 (2004) 161-169.
[with M. J. Grannell and T. S. Griggs], Configurations and trades in Steiner triple systems, The Australasian Journal of Combinatorics 29 (2004), 75-84.
Uniquely 3-colourable Steiner triple systems, J. Combin. Theory, Series A 101 (2003), 49-68.
[with M. J. Grannell and T. S. Griggs], On colourings of Steiner triple systems, Discrete Mathematics 261 (2003), 255-276.
Three Primes: Notes for talks given at London South Bank University, February 2012.
Congruence Properties of the Partition Function: Notes for talks given at London South Bank University, 24 September, 8 October and 19 November 2008.
Factorization of Integers: Notes for talks given at London South Bank University, 20 February and 19 March 2008.
Elliptic curves, Factorization and Primality Testing: Notes for talks given at London South Bank University, 7, 14 and 21 November 2007.
Titanic prime quintuplets, M500 189 (December 2002)
Gigantic prime triplets, M500 226 (February 2009)
Large prime quadruplets, Mathematical Gazette 84 no. 501 (November 2000), 447-452
Ten consecutive primes in arithmetic progression
Two hundred and fourteen primes in the vicinity of P = 100 99697 24697 14247 63778 66555 87969 84032 95093 24689 19004 18036 03417 75890 43417 03348 88215 90672 29719. Ten consecutive primes in arithmetic progression appear in a vertical line. The top one is P. The other nine are P + 210, P + 420, ..., P + 1890. See also: ⇒ Theorem of the Day Number 32, The Green-Tao Theorem on Primes in Arithmetic Progression. ⇒ Theorem of the Day Number 109, The Beardwood-Halton-Hammersley Theorem. ⇒ 2009 Calendar: 12 Theorems by Women Mathematicians. And there's Manfred Toplic's site at The Nine and Ten Primes Project.
Fifteen consecutive integers with exactly four prime factors, Math. Comp. 71 (2002), 449-452.
[with H. Dubner, N. Lygeros, M. Mizony, H. Nelson and P. Zimmermann], Ten Consecutive Primes in Arithmetic Progression, Math. Comp. 71 (2002), 1323-1328. Also available as a PDF file.
[with Harvey Dubner], Prime Pythagorean triangles, J. Integer Sequences 4 (2001), Article 01.2.3
Prime clusters and Cunningham chains, Math. Comp. 68 (1999), 1739-1747.
A large pair of twin primes, Math. Comp. 66 (1997), 451-455.
Congruence properties of functions related to the partition function, Pacific Journal of Mathematics 158 (1993), 145-156.
