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Publications

Books, chapters of books, papers in international journals, papers in peer-reviewed proceedings, preprints.
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    Books

  1. Residually weakly primitive and locally two-transitive geometries for sporadic groups. Acad. roy. Belgique, Mem. Cl. Sci., Coll. 4, Ser. 3, Tome XI(2008), 173pp.
  2. with F. Buekenhout and M. Dehon, An Atlas of Residually Weakly Primitive Geometries for Small Groups. Acad. roy. Belgique, Mem. Cl. Sci., Coll. 8, Ser. 3, Tome XIV(1999), 175 pp.

    3. Chapters in books

  3. with M.-E. Fernandes and A. Weiss, Hexagonal extensions of toroidal maps and hypermaps, M.D.E.Conder et al. (editors), Discrete Geometry and Symmetry, Dedicated to Karoly Bezdek and Egon Schulte on the Occasion of Their 60th Birthdays, Springer Proceedings in Mathematics and Statistics 234 (2018), 147-170.
  4. with I. Hubard, Chiral polytopes and Suzuki simple groups, In Eds. R. Connelly, W. Whitely, A. Weiss, Rigidity and Symmetry, Fields Institute Communications 70 (2014), 155-175.
  5. with F. Buekenhout, P. Cara and M. Dehon, Residually weakly primitive geometries of small sporadic and almost simple groups : a synthesis. In A. Pasini (editor), Topics in Diagram Geometry, Quaderni Mat. 12(2003), 1-27.
  6. Incidence Geometry. In W. Bosma and J. Cannon, Handbook of Magma Functions, Version 2.7 (July 2000), Vol. V, chapter 82, pp 335-359.

    7. Papers in international journals

  7. with G. Araujo-Pardo, M. Conder, N. Garcia-Colin and G. Kiss, A note on girth-diameter cages, Art Discrete Appl. Math., to appear, 6 pages.
  8. with M. Toledo, Faithful and thin non-polytopal maniplexes, Ars Math. Contemp., to appear, 12 pages.
  9. with K. Stokes and P. Tranchida, On trialities and their absolute geometries, Adv. Geom. 24, no. 4 (2024), 449-462.
  10. with N. Garcia-Colin, M. Muessig and E. Roldan-Roa, There is no perfect Mondrian partition for squares of side lengths less than 1001, Discrete Appl. Math. 359 (2024), 400-406.
  11. with P.J. Cameron and M.-E. Fernandes, The number of string C-groups of high rank, Adv. Math. 453 (2024), #109832, 49 pages.
  12. with J. De Saedeleer and J. Mulpas, A rank augmentation theorem for rank 3 string C-group representations of the symmetric groups, J. Algebraic Combin. 59 (2024), 393-411.
  13. with M. Toledo, Maniplexes with automorphism group PSL(2,q). Discrete Math. 346, nr. 9 (2023), #113527.
  14. with A. Betten, B. Muehlherr, J. Parkinson, K. Thas and H. Van Maldeghem, Preface to the Special Issue in Memoriam of Jacques Tits. Innov. Incidence Geom. 20, no. 2-3 (2023), 63-64.
  15. with K. Stokes, Incidence geometries with trialities coming from maps with Wilson trialities. Innov. Incidence Geom. 20, nr. 2-3 (2023), 325-340.
  16. with P. J. Cameron and A. Herman, String C-groups with real Schur index 2. J. Pure Appl. Algebra 226 (2022), #107025.
  17. with G. Araujo-Pardo, Edge-girth-regular graphs arising from biaffine planes and Suzuki groups. Discrete Math. 345 (2022), #112991.
  18. with J. Mulpas, The String C-group representations of the Suzuki, Rudvalis and O'Nan sporadic groups. Art Discrete Appl. Math. 5, nr. 3 (2022), Paper No. 3.09, 12pp.
  19. with A. Vandenschrick, On chiral polytopes having a group PSL(3,q) as automorphism group. J. London Math. Soc. (2) 106, nr. 1 (2022), 85-111.
  20. with F. Buekenhout and P. Tranchida, A new algorithm to classify chiral polytopes with a given automorphism group. Beitrage Algebra Geom. 62 (2021), 21-36.
  21. with P. Tranchida, On residual connectedness in chiral geometries. Algebr. Comb. 4, no. 3 (2021), 491-499.
  22. with N. Garcia-Colin, An infinite family of locally X graphs based on incidence geometries. Art Discrete Appl. Math. 4 (2021), #P3.01.
  23. with P. A. Brooksbank and J. T. Ferrara, Orthogonal groups in characteristic 2 acting on polytopes of high rank. Discrete Comput. Geom. 63 (2020), 656-669.
  24. with D. Hou and Y. Feng, On regular polytopes of 2-power order. Discrete Comput. Geom. 64, nr. 2 (2020), 339-346.
  25. with M. E. Fernandes and A. Ivic Weiss, An exploration of locally spherical regular hypertopes. Discrete Comput. Geom. 64, nr. 2 (2020), 519-534.
  26. with D. Hou and Y. Feng, Existence of regular 3-hypertopes with 2n chambers. Discrete Math. 342 (2019), 1857-1863.
  27. with D. Hou and Y. Feng, 2-groups behaving as automorphism groups of regular 3-polytopes. J. Group Theory 22 (2019), 579-616.
  28. with B.G.Rodrigues, On primitive geometries of rank two, Art Discrete Appl. Math. 2 (2019), #P1.08.
  29. with P. A. Brooksbank, Rank reduction of string C-group representations. Proc. Amer. Math. Soc. 147 (2019), 5421-5426.
  30. with M.-E. Fernandes, String C-group representations of alternating groups. Ars Math. Contemp. 17 (2019), 291-310.
  31. with E.Schulte and H.Van Maldeghem, Groups of Ree type in characteristic 3 acting on polytopes, Ars Math. Contemp. 14 (2018), 209-226.
  32. with M.-E.Fernandes, C-groups of high rank for the symmetric groups, J. Algebra 508 (2018), 196-218.
  33. with D. Catalano, M.-E.Fernandes and I. Hubard, Hypertopes with tetrahedral diagram. Elec. J. Combin. 25 no. 3 (2018), P3.22.
  34. with M.-E.Fernandes and M.Mixer, An extension of the classification of high rank regular polytopes, Trans. Amer. Math. Soc. 370 (2018), 8833-8857.
  35. with J. Moerenhout and E. O'Reilly-Regueiro, Projective linear groups as automorphism groups of chiral polytopes, J. Geom. 108 (2017), 672-702.
  36. with P.J.Cameron, M.-E.Fernandes and M.Mixer, Highest rank of a polytope for An, Proc. London Math. Soc. 115 (2017), 135-176.
  37. with M. W. Liebeck, Chiral polyhedra and finite simple groups, Bull. London Math. Soc. 49 (2017), 581-592.
  38. with T.Connor, Algorithmic enumeration of regular maps. Ars Math. Contemp. 10 (2016), 211-222.
  39. with P.J.Cameron, M.-E.Fernandes and M.Mixer, String C-groups as transitive subgroups of Sym(n), J. Algebra 447 (2016), 468-478.
  40. with P.A.Brooksbank, Polytopes of large rank for PSL(4,q), J. Algebra 452 (2016), 390-400.
  41. with F.Buekenhout and J.De Saedeleer, Two-transitive pairs in PSL(2,q). Bull. Belg. Math. Soc. - Simon Stevin 23 (2016), 33-55.
  42. with B.G.Rodrigues, Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graph, Math. Comm. 21 (2016), 239-249.
  43. with J. Moerenhout, Chiral polyhedra arising from almost simple groups with socle PSL(2,q), J. Algebraic Combin. 44 (2016), 293-323.
  44. with M.-E.Fernandes and A.Ivic-Weiss, Highly symmetric hypertopes, Aequationes Math. 90 (2016), 1045-1067.
  45. with T.Connor and J.De Saedeleer, Almost simple groups with socle PSL(2,q) acting on abstract regular polytopes, J. Algebra 423 (2015), 550-558.
  46. with T.Connor, An Atlas of subgroup lattices of finite almost simple groups. Ars Math. Contemp.8 (2015), 259-266.
  47. with T.Connor and S.Jambor, C-groups of PSL(2,q) and PGL(2,q), J. Algebra 427 (2015), 455-466.
  48. with D.Elliott and E.O'Reilly-Regueiro, Chiral polyhedra and projective lines, Int. J. Math. Stat. 16 (2015), 45-52.
  49. with T.Connor, C-groups of Suzuki type. J. Algebraic Combin. 42 (2015), 849-860.
  50. with T.Connor and M.Mixer, Abstract regular polytopes for the O'Nan group. International Journal of Algebra and Computation 24 (2014), nr. 1, 59-68.
  51. with J.De Saedeleer, M.Mixer and T.Pisanski, Core-free, rank two coset geometries from edge-transitive bipartite graphs, Math. Slovaca 64 (2014), 1-16.
  52. with W. Fan, C.H.Li and J.Pan, Locally 2-arc-transitive complete bipartite graphs. J. Combin. Theory Ser. A 120 (2013), 683-699.
  53. with B.G.Rodrigues, Binary codes of some strongly regular graphs of the McLaughlin graph. Designs, Codes, Crypto. 67 (2013), nr. 1, 93-109.
  54. with M.-E.Fernandes and M.Mixer, Corrigendum to "Polytopes of high rank for the symmetric groups", Adv. Math. 238 (2013), 506-508.
  55. with F.Buekenhout and J.De Saedeleer, The rank two geometries of the PSL(2,q) groups : part II. Ars Math. Contemp. 6 (2013), 365-388.
  56. with F.Buekenhout and J.De Saedeleer, The rank two geometries of the PSL(2,q) groups : part II, Appendix. Ars Math. Contemp. 6 (2013), A1-A21
  57. with T.Connor, A new algorithm to find apartments in coset geometries. Groups, Complexity, Cryptology 5 (2013), nr. 1, 75-89.
  58. with A.Kiefer, On pairs of commuting involutions in Sym(n) and Alt(n), Comm. Algebra 41 (2013), nr. 12, 4408-4418.
  59. with M.-E.Fernandes and M.Mixer, Polytopes of high rank for the alternating groups. J. Combin. Theory Ser. A 119 (2012), 42-56.
  60. with M. I. Hartley and I. Hubard, Regular 4-polytopes from the Livingstone graph of Janko's first group. J. Algebraic Combin. 35 (2012), 193-214.
  61. with M.-E.Fernandes and M.Mixer, All alternating groups An with n ≥ 12 have polytopes of rank ⌊ (n-1)/2 ⌋. SIAM Journal on Discrete Math. 26 (2012), nr. 2, 482-498.
  62. with M. I. Hartley and I. Hubard, Two atlases of abstract chiral polytopes for small groups. Ars Math. Contemp.5 (2012), 371-382.
  63. with M.Mixer, Algorithms for classifying regular polytopes with a fixed automorphism group, Contr. Discrete Math. 7 (2012), 105-118.
  64. with M.-E. Fernandes, Polytopes of high rank for the symmetric groups. Adv. Math. 228 (2011), 3207-3222.
  65. with P. Rowley, Rank three residually connected geometries for M_{22}, revisited. Elec. J. Combin. 17 (2010), nr. 4.
  66. with A. Kiefer, On the number of abstract regular polytopes whose automorphism group is a Suzuki simple group Sz(q). J. Combin. Theory Ser. A 117 (2010), 1248-1257.
  67. On the geometry of O'N. J. Geom. 97 (2010), 83-97.
  68. with J. De Saedeleer, On the rank two geometries of the PSL(2,q) groups : part I. Ars Math. Contemp. 3 (2010), 177-192.
  69. with M. I. Hartley, On locally spherical polytopes of type {5,3,5}. Discrete Math. 309(2009), 247-254.
  70. Locally s-arc-transitive graphs related to sporadic simple groups. J. Algebra 322(2009), 882-892.
  71. with E. Schulte, Polytopes with groups of type PGL(2,q). Ars Math. Contemp. 2(2009), 163-171.
  72. with F. Buekenhout, On apartments in incidence geometry. J. of Combinatorics, Information and System Sciences 34 (2009) No. 1-4, pages 75-93.
  73. with M. I. Hartley, A new Petrie-like construction for abstract polytopes. J. Combin. Theory Ser. A 115(2008), 997-1007.
  74. with F. Buekenhout, A rank six geometry related to the McLaughlin sporadic simple group . Designs, Codes, Crypto. 44(2007), nr. 1/2/3, 151-155.
  75. with E. Schulte, Groups of type L(2,q) acting on polytopes. Adv. Geom. 7(2007), nr. 4, 529-539.
  76. with M. I. Hartley, Errata : "Quotients of a universal locally projective polytope of type {5,3,5}". Math. Z. 253(2006), nr. 2, 433-434.
  77. Almost simple groups of Suzuki type acting on polytopes. Proc. Amer. Math. Soc. 134(2006), 3649-3651.
  78. with L. Vauthier, An atlas of abstract regular polytopes for small groups. Aequationes Math. 72(2006), nr. 3, 313-320.
  79. Two rank six geometries for the Higman-Sims sporadic group. Discrete Math. 294(2005), nr. 1-2, 123-132.
  80. with M.I. Hartley On the thin regular geometries of rank four for the Janko group J(1). Innov. Incidence Geom. 1(2005), 181-190.
  81. with P. Cara, On inductively minimal geometries that satisfy the intersection property. J. Combin. Theory Ser. A. 111 (2005), nr. 2, 327-330.
  82. A family of geometries related to the Suzuki tower. Comm. Algebra 33 (2005), nr. 7, 2201-2217.
  83. The residually weakly primitive geometries of HS. Australas. J. Combin. 33 (2005), 231-236.
  84. A generalization of a construction due to Van Nypelseer. Beitrage Algebra Geom. 46 (2005), nr. 2, 561-574.
  85. Constructions of rank five geometries for the Mathieu group M_22. J. Geom. 79(2004), nr. 1-2, 146-155.
  86. with M. Gailly, The residually weakly primitive geometries of PSL(3,q) with q < 8. Aequationes Math. 67(2004), 195-196.
  87. with M. I. Hartley, Quotients of a universal locally projective polytope of type {5,3,5}. Math. Z. 247(2004), nr. 4, 663-674.
  88. with P. Jacobs, An algorithmic analysis of the intersection property. LMS J. Comput. Math. 7(2004), 284-299.
  89. The residually weakly primitive geometries of J_3. Experiment. Math. 13(2004), nr. 4, 429-433.
  90. The residually weakly primitive geometries of M_23. Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia LII(2004), 313-316.
  91. On a rank four geometry for the Hall-Janko sporadic group. J. Combin. Theory Ser. A 101(2003), nr. 1, 160-167.
  92. with H. Gottschalk, Geometries for the group PSL(3,4). European J. Combin. 24(2003), nr. 3, 267-291.
  93. The residually weakly primitive geometries of M_22. Designs, Codes, Crypto. 29(2003), nr. 1/2/3, 177-178.
  94. with F. Buekenhout and P.-O. Dehaye, RWPRI and (2T)_1 flag-transitive linear spaces. Beitrage Algebra Geom. 44(2003), nr. 1, 25-46.
  95. with P.Cara, The RWPRI geometries of Sym(5) x 2. Discrete Math. 255(2002), nr. 1/3, 35-45. MR 2003i:51012.
  96. The residually weakly primitive geometries of J_2. Note Mat. 21(2002), nr. 1, 77-81.
  97. with M. Dehon, Constructing coset geometries with Magma : An application to the sporadic groups M(12) and J(1). Atti Sem. Mat. Fis. Univ. Modena L(2002), 415-427.
  98. On a rank five geometry of Meixner for the Mathieu group M(12). Geom. Dedicata 85(2001), nr. 1/3, 273-281. MR 2002f: 51021. Zbl 0989.51007.
  99. Some rank five geometries related to the Mathieu group M(23). J. Combin. Theory Ser. A 95(2001), nr. 2, 365-372. MR 2002d: 51011. Zbl 0990.51005.
  100. with D.Bonheure and F.Buekenhout, On the Petrials of thin regular rank three geometries. J. Geom. 71(2001), nr. 1-2, 19- 26. MR 2002g:51014. Zbl 1013.51005.
  101. The residually weakly primitive geometries of the Dihedral Groups. Atti Sem. Mat. Fis. Univ. Modena XLVIII(2000), 179-190. MR 2001e:05027. Zbl. 0967.51002.
  102. The residually weakly primitive pre-geometries of the Suzuki simple groups. Note Mat.20(2000), no. 1, 15-34. MR 2003b:51021.
  103. with C.Lefèvre-Percsy and N.Percsy, New geometries for finite groups and polytopes. Bull. Belg. Math. Soc. - Simon Stevin 7(2000), nr. 4, 583-610. MR 2001m:51020. Zbl 0974.51011.
  104. with F.Buekenhout, On a geometry of Ivanov and Shpectorov for the O'Nan sporadic simple group. J. Combin. Theory Ser. A 85(1999), nr. 2, 148-164. MR 2000a:51014. Zbl 930.20014.
  105. An Atlas of regular thin geometries for small groups. Math. Comput. 68(1999), nr. 228, 1631-1647. MR 99m:51018. Zbl 941.51010.
  106. The rank 3 geometries of the simple Suzuki groups Sz(q). Note Mat. 19(1999), no. 1, 43-63. MR 2001m:51019.
  107. The Rank 2 Geometries of the Simple Suzuki Groups Sz(q). Beitrage Algebra Geom. 39(1998), nr.1, 97-120. MR 99b:20030. Zbl 914.51009.
  108. Thin geometries for the Suzuki simple group Sz(8). Bull. Belg. Math. Soc. - Simon Stevin 5(1998), nr. 2-3, 373-387. MR 99f:51021. Zbl 930.51009.
  109. Two Nearly Isomorphic Groups. Atti Sem. Mat. Fis. Univ. Modena XLV(1997), 373-376. MR 98k:20005. Zbl 893.20001.
  110. with F.Buekenhout, On the List of Finite Primitive Permutation Groups of Degree Less Than 50. J. Symbolic Comput. 22(1996), 215-225. MR 97g:20004. Zbl 870.20003.
  111. with F.Buekenhout and M.Dehon, All Geometries of the Mathieu Group M(11) Based on Maximal Subgroups. Experiment. Math. 5(1996), nr.2, 101-110. MR 97h:51015. Zbl 863.51012.

    112. Papers in proceedings (peer-reviewed)

  112. String C-group representations of almost simple groups: a survey. In G. Cunningham, M. Mixer and E. Schulte (eds), Polytopes and Discrete Geometry, Contemp. Math. 764 (2021), 157-178.
  113. with M. E. Fernandes, C. A. Piedade and A. Ivic Weiss, Two families of locally toroidal regular 4-hypertopes arising from toroids. In G. Cunningham, M. Mixer and E. Schulte (eds), Polytopes and Discrete Geometry, Contemp. Math. 764 (2021), 89-100.
  114. with K. Stokes, Coset geometries with trialities and their reduced incidence graphs. Acta Math. Univ. Comenianae 89 (2019), 911-916.
  115. The residually weakly primitive geometries of the Suzuki simple group Sz(8), In C.M. Campbell, E.F. Robertson, N. Ruskuc, G.C. Smith (editors), Groups St Andrews 1997 in Bath, II. London Math. Soc. Lect. Notes Ser. 261(1999), 517-526. MR 2000h:51025. Zbl. 934.51009.
  116. with F.Buekenhout and M.Dehon, On Flag-Transitive Incidence Geometries of Rank 6 for the Mathieu Group M(12). In L. Di Martino, W.E. Kantor, G. Lunardon, A. Pasini (editors), Groups and Geometries, Trends in Math., 1998, 39-54. MR 99m:51017. Zbl 899.51006.
  117. with H.Gottschalk, The Residually Weakly Primitive Geometries of the Janko Group J(1). In L. Di Martino, W.E. Kantor, G. Lunardon, A. Pasini (editors), Groups and Geometries, Trends in Math., 1998, 65-79. MR 99h:51014. Zbl 902.51006.

    Preprints

  1. with K. Stokes and P. Tranchida, Flag transitive geometries with trialities and no dualities coming from Suzuki groups, 14 pages.
  2. with D. Hou and Y. Feng, Regular 3-polytopes of order 2np. 17 pages.
  3. with D. Hou, Y. Feng and H.-P. Qu, String C-groups of order 4pm, 12 pages.

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