Leonard Soicher's publications

Software packages (current versions)

• L.H. Soicher, The GRAPE package for GAP, Version 4.9.2, 2024, https://gap-packages.github.io/grape
• L.H. Soicher, The DESIGN package for GAP, Version 1.8.2, 2024, https://gap-packages.github.io/design
• L.H. Soicher, The tcenum coset enumeration package, Version 1.0.0, 2024, https://github.com/lhsoicher/tcenum/releases/tag/v1.0.0

Submitted

• L.H. Soicher, The non-synchronizing primitive groups of degree up to 624, submitted for publication. Preprint available at https://doi.org/10.48550/arXiv.2412.10903

2024

• L.H. Soicher, Software for proper vertex-colouring exploiting graph symmetry, in Mathematical Software - ICMS 2024 (K. Buzzard et al., eds), Lecture Notes in Computer Science 14749, Springer, 2024, pp. 106-112. accepted manuscript
• L.H. Soicher, Using GAP packages for research in graph theory, design theory, and finite geometry, in Algebraic Combinatorics and the Monster Group (A.A. Ivanov, ed.), London Math. Soc. Lecture Note Series 487, Cambridge University Press, 2024, pp. 527-566. accepted manuscript

2022

• L.H. Soicher, Obituary of John McKay, London Mathematical Society Newsletter, Issue 503, November 2022, 44-45.

2021

• R.A. Bailey and L.H. Soicher, Uniform semi-Latin squares and their pairwise-variance aberrations, Journal of Statistical Planning and Inference 213 (2021), 282-291. DOI: 10.1016/j.jspi.2020.12.003 Accepted manuscript available at https://arxiv.org/abs/2008.10552

2020

• R.A. Bailey, P.J. Cameron, L.H. Soicher and E.R. Williams, Substitutes for the non-existent square lattice designs for 36 varieties, Journal of Agricultural, Biological and Environmental Statistics 25 (2020), 487-499. Available online (open-access) at https://doi.org/10.1007/s13253-020-00388-1

2018

• G.R.W. Greaves and L.H. Soicher, On the clique number of a strongly regular graph, Electron. J. Combin. 25 (2018), #P4.15, 15pp.
• P.R.J. Östergård and L.H. Soicher, There is no McLaughlin geometry, J. Comb. Theory, Ser. A 155 (2018), 27-41. Preprint available at http://arxiv.org/abs/1607.03372

2017

• L.H. Soicher, On classifying objects with specified groups of automorphisms, friendly subgroups, and Sylow tower groups, Port. Math. 74 (2017), 233-242. revised PDF preprint.
• L.H. Soicher, The uniqueness of a distance-regular graph with intersection array {32,27,8,1;1,4,27,32} and related results, Des. Codes Cryptogr. 84 (2017), 101-108. Available online (open-access) at http://dx.doi.org/10.1007/s10623-016-0223-6

2016

• V. Linek, L.H. Soicher and B. Stevens, Cube designs, J. Combin. Des. 24 (2016), 223-233. PDF preprint.

2015

• L.H. Soicher, On cliques in edge-regular graphs, J. Algebra 421 (2015), 260-267. revised PDF preprint.

2013

• L.H. Soicher, Designs, groups and computing, in Probabilistic Group Theory, Combinatorics, and Computing. Lectures from the Fifth de Brún Workshop, A. Detinko et al. (eds), Lecture Notes in Mathematics 2070, Springer, 2013, 83-107. revised PDF preprint.

• L.H. Soicher, Optimal and efficient semi-Latin squares, J. Statist. Plann. Inference 143 (2013), 573-582. revised PDF preprint.

2012

• L.H. Soicher, Uniform semi-Latin squares and their Schur-optimality, J. Combin. Des. 20 (2012), 265-277. PDF preprint.

2011

• L.H. Soicher, On generalised t-designs and their parameters, Discrete Math. 311 (2011), 1136-1141. PDF preprint.

2010

• L.H. Soicher, More on block intersection polynomials and new applications to graphs and block designs, J. Comb. Theory, Ser. A 117 (2010), 799-809. PDF preprint.

2007

• P.J. Cameron and L.H. Soicher, Block intersection polynomials, Bull. London Math. Soc. 39 (2007), 559-564. PDF preprint.

• J.P. McSorley and L.H. Soicher, Constructing t-designs from t-wise balanced designs, European J. Combinatorics 28 (2007), 567-571. PDF preprint.

• P. Dobcsányi, D.A. Preece and L.H. Soicher, On balanced incomplete-block designs with repeated blocks, European J. Combinatorics 28 (2007), 1955-1970. PDF preprint.

2006

• R.A. Bailey, P.J. Cameron, P. Dobcsányi, J.P. Morgan and L.H. Soicher, Designs on the web, Discrete Math. 306 (2006), 3014-3027. PDF preprint.

• L.H. Soicher, Is there a McLaughlin geometry?, J. Algebra 300 (2006), 248-255. PDF preprint. Log-file of the GAP/GRAPE computations.

• L.H. Soicher, Computational group theory problems arising from computational design theory, Oberwolfach Rep. 3 (2006), Report 30/2006: Computational group theory, 1809-1811. PDF preprint.

2004

• L.H. Soicher, Computing with graphs and groups, in Topics in Algebraic Graph Theory (L.W. Beineke and R.J. Wilson, eds), Cambridge University Press, 2004, pp. 250-266. PDF preprint.

• L. Soicher and F. Vivaldi, Algorithmic Mathematics, web-book, 2004.

2003

• L.H. Soicher, GRAPE, in Computer Algebra Handbook: Foundations, Applications, Systems (J. Grabmeier, E. Kaltofen and V. Weispfenning, eds), Springer, Berlin, 2003, pp. 473-474.

• P.J. Cameron, P. Dobcsányi, J.P. Morgan and L.H. Soicher, The External Representation of Block Designs, 2003.

2001

• G. Havas, L.H. Soicher and R.A. Wilson, A presentation for the Thompson sporadic simple group, in Groups and Computation III (W.M. Kantor and Á Seress, eds), Ohio State Univ. Math. Res. Inst. Publ. 8, de Gruyter, Berlin, 2001, pp. 193-200. The article in PostScript. The matrices a, b, c, d, e, s, t, u in GAP format.

2000

• S. Rees and L.H. Soicher, An algorithmic approach to fundamental groups and covers of combinatorial cell complexes, J. Symbolic Comp. 29 (2000), 59-77. An implementation of the algorithms for simplicial complexes.

• N.A. Gordon, R. Shaw and L.H. Soicher, Classification of partial spreads in PG(4,2), Mathematics Research Reports (University of Hull) XIII (2000), No.1. The article in PostScript.

• L.H. Soicher, Computation of partial spreads, www-preprint, 2000.

• L.H. Soicher, SOMA Update, www-preprint, 2000.

1999

• H. Cuypers, L.H. Soicher and H. Sterk, Working with finite groups, in Some Tapas of Computer Algebra (A.M. Cohen, H. Cuypers and H. Sterk, eds), Springer, Berlin, 1999, pp. 184-207.

• H. Cuypers, L.H. Soicher and H. Sterk, The small Mathieu groups (Project), in Some Tapas of Computer Algebra (A.M. Cohen, H. Cuypers and H. Sterk, eds), Springer, Berlin, 1999, pp. 323-337.

• L.H. Soicher, On the structure and classification of SOMAs: generalizations of mutually orthogonal Latin squares, Electron. J. Combin. 6 (1999), #R32, 15pp.

1998

• C.R. Leedham-Green and L.H. Soicher, Symbolic collection using Deep Thought, London Math. Soc. J. Comput. Math. 1 (1998), 9-24.

1997

• C.E. Praeger and L.H. Soicher, Low Rank Representations and Graphs for Sporadic Groups, Australian Math. Soc. Lecture Series 8, Cambridge University Press, 1997. xi+141 pp.

1995

• J.I. Hall and L.H. Soicher, Presentations of some 3-transposition groups, Comm. Algebra 23 (1995), 2517-2559.

• A.A. Ivanov, S.A. Linton, K. Lux, J.Saxl and L.H. Soicher, Distance-transitive representations of the sporadic groups, Comm. Algebra 23 (1995), 3379-3427.

• S.A. Linton, K. Lux and L.H. Soicher, The primitive distance-transitive representations of the Fischer groups, Experimental Math. 4 (1995), 235-253.

• L.H. Soicher, Yet another distance-regular graph related to a Golay code, Electron. J. Combin. 2 (1995), #N1, 4pp.

1994

• L.H. Soicher, Coset enumeration, permutation group algorithms, and applications to graphs and geometries,in EIDMA Minicourse, Computer Algebra with emphasis on discrete algebra and geometry, Eindhoven, 1994. The article in PostScript.

1993

• L.H. Soicher, Three new distance-regular graphs, Europ. J. Combinatorics 14 (1993), 501-505.

• L.H. Soicher, GRAPE: A system for computing with graphs and groups, in Groups and Computation (L. Finkelstein and W.M. Kantor, eds), DIMACS Series in Discrete Math. and Theoretical Comp. Sci. 11, AMS, Providence, 1993, pp. 287-291.

• L.H. Soicher, The Lyons group has no distance-transitive representation, in Finite Geometry and Combinatorics, (F. DeClerck et al., eds), London Math. Soc. Lecture Note Series 191, Cambridge University Press, 1993, pp. 355-358.

1992

• L.H. Soicher, On simplicial complexes related to the Suzuki sequence graphs, in Groups, Combinatorics and Geometry (M.W. Liebeck and J. Saxl, eds), London Math. Soc. Lecture Note Series 165, Cambridge University Press, 1992, pp. 240-248.

1991

• L.H. Soicher, More on the group Y₅₅₅ and the projective plane of order 3, J. Algebra 136 (1991), 168-174.

• L.H. Soicher, A new uniqueness proof for the Held group, Bull. London Math. Soc. 23 (1991), 235-238.

• C.R. Leedham-Green, C.E. Praeger and L.H. Soicher, Computing with group homomorphisms, J. Symbolic Comp. 12 (1991), 527-532.

1990

• L.H. Soicher, A new existence and uniqueness proof for the O'Nan group, Bull. London Math. Soc. 22 (1990), 148-152.

• C.R. Leedham-Green and L.H. Soicher, Collection from the left and other strategies, J. Symbolic Comp. 9 (1990), 665-675.

1989

• L.H. Soicher, From the Monster to the Bimonster, J. Algebra 121 (1989), 275-280.

1988

• J.H. Conway, S.P. Norton and L.H. Soicher, The Bimonster, the group Y₅₅₅, and the projective plane of order 3, in Computers in Algebra (M. Tangora, ed.), Marcel Dekker, New York, 1988, 27-50.

• L.H. Soicher, Presentations for some groups related to Co₁, in Computers in Algebra (M. Tangora, ed.), Marcel Dekker, New York, 1988, 151-154.

1987

• L.H. Soicher, Presentations of some finite groups with applications to the O'Nan simple group, J. Algebra 108 (1987), 310-316.

• L.H. Soicher, Presentations for Conway's group Co₁, Math. Proc. Camb. Phil. Soc. 102 (1987), 1-3.

1985

• L.H. Soicher, Presentations of Some Finite Groups, PhD Thesis, University of Cambridge, 1985. doi.org/10.17863/CAM.110463

• L. Soicher and J. McKay, Computing Galois groups over the rationals, J. Number Theory 20 (1985), 273-281.

1984

• L.H. Soicher, An algorithm for computing Galois groups, in Computational Group Theory (M.D.Atkinson, ed.), Academic Press, London, 1984, 291-296.

1982

• C.W.H. Lam and L.H. Soicher, Three new combination algorithms with the minimal change property, Comm. Assoc. Comput. Mach. 25 (1982), 555-559.

1981

• L. Soicher, The Computation of Galois Groups, M.Comp.Sci. Thesis, Concordia University, Montreal, 1981. PDF of scanned copy.