메뉴 건너뛰기




Volumn , Issue , 2009, Pages 67-112

Siamese combinatorial objects via computer algebra experimentation

Author keywords

Association scheme; Coherent configuration; Color graph; Computer algebra package; Distance regular graph; Generalized quadrangle; Siamese association scheme; Siamese color graph; Siamese Steiner design; Spread; Steiner system; Strongly regular graph

Indexed keywords


EID: 80053634374     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-01960-9_2     Document Type: Chapter
Times cited : (7)

References (67)
  • 5
    • 18544409723 scopus 로고    scopus 로고
    • Graphical t-designs via kramer-mesner matrices
    • A. Betten, M. Klin, R. Laue, and A. Wasserman, Graphical t-designs via Kramer-Mesner matrices, Discrete Math., 197/198 (1999), 83-109.
    • (1999) Discrete Math. , vol.197-198 , pp. 83-109
    • Betten, A.1    Klin, M.2    Laue, R.3    Wasserman, A.4
  • 7
    • 33745807040 scopus 로고
    • Distance-regular graphs with diameter three
    • N. L. Biggs, Distance-regular graphs with diameter three, Ann. Discrete Math., 15 (1982), 69-80.
    • (1982) Ann. Discrete Math. , vol.15 , pp. 69-80
    • Biggs, N.L.1
  • 10
    • 84867976073 scopus 로고    scopus 로고
    • A root graph that is locally the line graph of the petersen graph
    • A. E. Brouwer, J. H. Koolen, and M. H. Klin, A root graph that is locally the line graph of the Petersen graph, Discrete Math., 264 (2003), 13-24.
    • (2003) Discrete Math. , vol.264 , pp. 13-24
    • Brouwer, A.E.1    Koolen, J.H.2    Klin, M.H.3
  • 11
    • 38249000754 scopus 로고
    • The transitive groups of degree fourteen and fifteen
    • G. Butler, The transitive groups of degree fourteen and fifteen, J. Symbol. Comput., 16 (1993), 413-422.
    • (1993) J. Symbol. Comput. , vol.16 , pp. 413-422
    • Butler, G.1
  • 12
    • 0004168878 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge
    • P. J. Cameron, Permutation Groups, Cambridge University Press, Cambridge, 1999.
    • (1999) Permutation Groups
    • Cameron, P.J.1
  • 13
    • 5644224357 scopus 로고
    • Complete classification of the triad systems of 15 elements
    • F. N. Cole, L. D. Cummings, and H. S. White, Complete classification of the triad systems of 15 elements, Proc. Nat. Acad. Sci. USA, 3 (1919), 197-199.
    • (1919) Proc. Nat. Acad. Sci. USA , vol.3 , pp. 197-199
    • Cole, F.N.1    Cummings, L.D.2    White, H.S.3
  • 15
    • 25444480492 scopus 로고    scopus 로고
    • Classification of three-class association schemes using backtracking with dynamic variable ordering
    • J. Degraer and K. Coolsaet, Classification of three-class association schemes using backtracking with dynamic variable ordering, Discrete Math., 300 (2005), 71-81.
    • (2005) Discrete Math. , vol.300 , pp. 71-81
    • Degraer, J.1    Coolsaet, K.2
  • 16
    • 0012755694 scopus 로고
    • Maximal subgroups of symplectic groups stabilizing spreads II
    • R. H. Dye, Maximal subgroups of symplectic groups stabilizing spreads II, Journal of London Math. Society (40), 2 (1989), 215-226.
    • (1989) Journal of London Math. Society , vol.2 , Issue.40 , pp. 215-226
    • Dye, R.H.1
  • 17
    • 85020563850 scopus 로고
    • Computer package for computations with coherent configurations
    • S. M. Wat (ed.) Assoc. Comput. Math. Press, New York
    • I. A. Faradžev and M. H. Klin, Computer package for computations with coherent configurations, in S. M. Wat (ed.) Proceedings ISSAC-91 Bonn, pp. 219-223, Assoc. Comput. Math. Press, New York, 1991.
    • (1991) Proceedings isSAC-91 Bonn , pp. 219-223
    • Faradžev, I.A.1    Klin, M.H.2
  • 18
    • 0002409906 scopus 로고
    • Cellular rings and groups of automorphisms of graphs
    • I. A. Faradžev, A. A. Ivanov, M. H. Klin and A. J. Woldar (eds.) Mathematics and Its Applications Kluwer Academic, Dordrecht
    • I. A. Faradžev, M. H. Klin, and M. E. Muzichuk, Cellular rings and groups of automorphisms of graphs, in I. A. Faradžev, A. A. Ivanov, M. H. Klin and A. J. Woldar (eds.) Investigations in Algebraic Theory of Combinatorial Objects. Mathematics and Its Applications, Vol. 84, pp. 1-152, Kluwer Academic, Dordrecht, 1994.
    • (1994) Investigations in Algebraic Theory of Combinatorial Objects , vol.84 , pp. 1-152
    • Faradžev, I.A.1    Klin, M.H.2    Muzichuk, M.E.3
  • 19
    • 0010851239 scopus 로고
    • An examination of the different possible solutions of a problem in incomplete blocks
    • R. A. Fisher, An examination of the different possible solutions of a problem in incomplete blocks, Ann. Eugenics, 10 (1940), 52-75.
    • (1940) Ann. Eugenics , vol.10 , pp. 52-75
    • Fisher, R.A.1
  • 21
    • 0002539270 scopus 로고
    • Construction methods for bhaskar rao and related designs
    • P. B. Gibbons and R. Mathon, Construction methods for Bhaskar Rao and related designs, J. Austral. Math. Soc., Ser. A, 42 (1987), 5-30.
    • (1987) J. Austral. Math. Soc., Ser. A , vol.42 , pp. 5-30
    • Gibbons, P.B.1    Mathon, R.2
  • 22
    • 38249010739 scopus 로고
    • Distance regular covers of complete graphs
    • C. D. Godsil and A. D. Hensel, Distance regular covers of complete graphs, J. Comb. Theory, Ser. B, 36 (1992), 205-238.
    • (1992) J. Comb. Theory, Ser. B , vol.36 , pp. 205-238
    • Godsil, C.D.1    Hensel, A.D.2
  • 23
    • 0038846152 scopus 로고
    • Amorphic cellular rings
    • I. A. Faradžev, A. A. Ivanov, M. H. Klin, and A. J. Woldar (eds.) Mathematics and Its Applications Kluwer Academic, Dordrecht Translated from Russian
    • Ja. Ju. Gol'fand, A. V. Ivanov, and M. H. Klin, Amorphic cellular rings, in I. A. Faradžev, A. A. Ivanov, M. H. Klin, and A. J. Woldar (eds.) Investigations in Algebraic Theory of Combinatorial Objects. Mathematics and Its Applications, Vol. 84, pp. 167-186, Kluwer Academic, Dordrecht, 1994. Translated from Russian.
    • (1994) Investigations in Algebraic Theory of Combinatorial Objects , vol.84 , pp. 167-186
    • Gol'fand, Ja.Ju.1    Ivanov, A.V.2    Klin, M.H.3
  • 25
    • 0037845187 scopus 로고    scopus 로고
    • Maximal arcs in steiner systems S(2, 4, v). Combinatorics 2000 (Gaeta)
    • M. Greig and A. Rosa, Maximal arcs in Steiner systems S(2, 4, v). Combinatorics 2000 (Gaeta), Discrete Math. (1-3), 267 (2003), 143-151.
    • (2003) Discrete Math. , vol.267 , Issue.1-3 , pp. 143-151
    • Greig, M.1    Rosa, A.2
  • 27
    • 84968520221 scopus 로고
    • Determination of steiner triple systems of order 15
    • M. Hall and J. D. Swift, Determination of Steiner triple systems of order 15, Math. Tables Other Aids Comput., 9 (1955), 146-152.
    • (1955) Math. Tables Other Aids Comput. , vol.9 , pp. 146-152
    • Hall, M.1    Swift, J.D.2
  • 28
    • 0003780715 scopus 로고
    • Addison-Wesley, Reading
    • F. Harary, Graph Theory, Addison-Wesley, Reading, 1969.
    • (1969) Graph Theory
    • Harary, F.1
  • 31
  • 32
    • 0013247325 scopus 로고    scopus 로고
    • A technique for constructing symmetric designs
    • Y. J. Ionin, A technique for constructing symmetric designs, Designs Codes Cryptogr., 14 (1998), 147-158.
    • (1998) Designs Codes Cryptogr. , vol.14 , pp. 147-158
    • Ionin, Y.J.1
  • 33
    • 84885797282 scopus 로고
    • Construction of some new automorphic graphs using computers
    • (in Russian)
    • A. A. Ivanov, Construction of some new automorphic graphs using computers, in Air Physics and Applied Mathematics (Moscow) MPhTI, pp. 144-146, 1981 (in Russian).
    • (1981) Air Physics and Applied Mathematics (Moscow) MPhTI , pp. 144-146
    • Ivanov, A.A.1
  • 34
    • 0012063085 scopus 로고    scopus 로고
    • Group actions, double cosets and homomorphisms: Unifying concepts for the constructive theory of discrete structures
    • M. Hazewinkel, A. A. Ivanov, and A. J. Woldar (eds.) Kluwer Academic, Dordrecht
    • A. Kerber and R. Laue, Group actions, double cosets and homomorphisms: Unifying concepts for the constructive theory of discrete structures, in M. Hazewinkel, A. A. Ivanov, and A. J. Woldar (eds.) Algebra and Combinatorics: Interactions and Applications. Acta Applicandae Mathematicae, Vol. 52 (1-3), pp. 63-90, Kluwer Academic, Dordrecht, 1998.
    • (1998) Algebra and Combinatorics: Interactions and Applications. Acta Applicandae Mathematicae , vol.52 , Issue.1-3 , pp. 63-90
    • Kerber, A.1    Laue, R.2
  • 35
    • 0347568561 scopus 로고    scopus 로고
    • On a decomposition of complete graphs
    • H. Kharaghani and R. Torabi, On a decomposition of complete graphs, Graphs Comb., 19 (2003), 519-526.
    • (2003) Graphs Comb. , vol.19 , pp. 519-526
    • Kharaghani, H.1    Torabi, R.2
  • 38
    • 84885734391 scopus 로고    scopus 로고
    • Siamese association schemes in miniature: A link between generalized quadrangles, graphs and steiner designs
    • M. H. Klin and S. Reichard, Siamese association schemes in miniature: A link between generalized quadrangles, graphs and Steiner designs. Abstracts of AMS Meeting (Bloomington), 2003, 985-05-232.
    • (2003) Abstracts of AMS Meeting (Bloomington) , pp. 985-05232
    • Klin, M.H.1    Reichard, S.2
  • 39
    • 33745810542 scopus 로고    scopus 로고
    • Siamese objects and their relation to color graphs, association schemes and steiner designs
    • M. H. Klin, R. Reichard, and A. J. Woldar, Siamese objects and their relation to color graphs, association schemes and Steiner designs, Bull. Belgian Math. Soc. (5), 12 (2005), 845-857.
    • (2005) Bull. Belgian Math. Soc. , vol.12 , Issue.5 , pp. 845-857
    • Klin, M.H.1    Reichard, R.2    Woldar, A.J.3
  • 42
    • 0002261718 scopus 로고    scopus 로고
    • Algebraic combinatorics in mathematical chemistry. Methods and algorithms. I. Permutation groups and coherent (cellular) algebras
    • M. Klin, C. Rücker, G. Rücker, and G. Tinhofer, Algebraic combinatorics in mathematical chemistry. Methods and algorithms. I. Permutation groups and coherent (cellular) algebras. MATCH, 40 (1999), 7-138.
    • (1999) MATCH , vol.40 , pp. 7-138
    • Klin, M.1    Rücker, C.2    Rücker, G.3    Tinhofer, G.4
  • 43
    • 0038575550 scopus 로고
    • T-designs on hypergraphs
    • E. S. Kramer and D. M. Mesner, t-Designs on hypergraphs, Discrete Math., 15 (1976), 263-296.
    • (1976) Discrete Math. , vol.15 , pp. 263-296
    • Kramer, E.S.1    Mesner, D.M.2
  • 44
    • 2342489864 scopus 로고
    • On imprimitive substitution groups
    • H. W. Kuhn, On imprimitive substitution groups, Am. J. Math., 26 (1904), 45-102.
    • (1904) Am. J. Math. , vol.26 , pp. 45-102
    • Kuhn, H.W.1
  • 45
    • 0020238702 scopus 로고
    • Computing double coset representatives for the generation of solvable groups
    • R. Laue, Computing double coset representatives for the generation of solvable groups, Lect. Notes Comput. Sci., 144 (1982), 65-70.
    • (1982) Lect. Notes Comput. Sci. , vol.144 , pp. 65-70
    • Laue, R.1
  • 46
    • 0038720370 scopus 로고
    • On the imprimitive substitution groups of degree fifteen and the primitive substitution groups of degree eighteen
    • E. N. Martin, On the imprimitive substitution groups of degree fifteen and the primitive substitution groups of degree eighteen, Am. J. Math., 23 (1901), 259-286.
    • (1901) Am. J. Math. , vol.23 , pp. 259-286
    • Martin, E.N.1
  • 47
    • 38249035869 scopus 로고
    • Lower bounds for ramsey numbers and association schemes
    • R. Mathon, Lower bounds for Ramsey numbers and association schemes, J. Comb. Theory, Ser. B, 42 (1987), 122-127.
    • (1987) J. Comb. Theory, Ser. B , vol.42 , pp. 122-127
    • Mathon, R.1
  • 48
    • 0002292058 scopus 로고
    • Small steiner triple systems and their properties
    • R. A. Mathon, K. T. Phelps, and A. Rosa, Small Steiner triple systems and their properties, Ars Combinatoria, 15 (1983), 3-110.
    • (1983) Ars Combinatoria , vol.15 , pp. 3-110
    • Mathon, R.A.1    Phelps, K.T.2    Rosa, A.3
  • 50
    • 0035964588 scopus 로고    scopus 로고
    • Colouring steiner systems with specified block colour patterns
    • S. Milici, A. Rosa, and V. Voloshin, Colouring Steiner systems with specified block colour patterns, Discrete Math. (1-3), 240 (2001), 145-160.
    • (2001) Discrete Math. , vol.240 , Issue.1-3 , pp. 145-160
    • Milici, S.1    Rosa, A.2    Voloshin, V.3
  • 51
    • 0001163683 scopus 로고
    • Tactical memoranda I-III
    • E. H. Moore, Tactical memoranda I-III, Am. J. Math., 18 (1896), 264-303.
    • (1896) Am. J. Math. , vol.18 , pp. 264-303
    • Moore, E.H.1
  • 52
    • 49549142231 scopus 로고
    • All generalized quadrangles of order 3 are known
    • S. E. Payne, All generalized quadrangles of order 3 are known, J. Comb. Theory, 18 (1975), 203-206.
    • (1975) J. Comb. Theory , vol.18 , pp. 203-206
    • Payne, S.E.1
  • 53
    • 0009036006 scopus 로고
    • Tight point sets in finite generalized quadrangles
    • S. E. Payne, Tight point sets in finite generalized quadrangles, Congressus Numerantium, 60 (1987), 243-260.
    • (1987) Congressus Numerantium , vol.60 , pp. 243-260
    • Payne, S.E.1
  • 56
    • 70349965251 scopus 로고
    • Über Untergruppen direkter Produkte von drei Faktoren
    • R. Remak, Über Untergruppen direkter Produkte von drei Faktoren, Crelle's J. Reine Angewandte Math., 166 (1931), 65-100.
    • (1931) Crelle's J. Reine Angewandte Math. , vol.166 , pp. 65-100
    • Remak, R.1
  • 57
    • 0039783204 scopus 로고
    • Thesis, Universität Bayreuth, Bayreuther Mathematische Schriften
    • B. Schmalz, t-Designs zu vorgegebener Automorphismengruppe, Thesis, Universität Bayreuth, Bayreuther Mathematische Schriften, 41 (1992), 1-164.
    • (1992) T-Designs Zu Vorgegebener Automorphismengruppe , vol.41 , pp. 1-164
    • Schmalz, B.1
  • 58
    • 84986440299 scopus 로고
    • The t-designs with prescribed automorphism group, new simple 6-designs
    • B. Schmalz, The t-designs with prescribed automorphism group, new simple 6-designs, J. Comb. Des., 1 (1993), 126-170.
    • (1993) J. Comb. Des. , vol.1 , pp. 126-170
    • Schmalz, B.1
  • 59
    • 0003591467 scopus 로고
    • Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen
    • M. Schönert et al., GAP-Groups, Algorithms, and Programming, Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen, 1995.
    • (1995) GAP-Groups, Algorithms, and Programming
    • Schönert, M.1
  • 63
    • 84885779892 scopus 로고    scopus 로고
    • E. Spence, http://www.maths.gla.ac.uk/~es/srgraphs.html.
    • Spence, E.1
  • 64
    • 0003014881 scopus 로고
    • Elementary researches in the analysis of combinatorial aggregation
    • J. J. Sylvester, Elementary researches in the analysis of combinatorial aggregation, Philos. Mag., 24 (1844), 285-296.
    • (1844) Philos. Mag. , vol.24 , pp. 285-296
    • Sylvester, J.J.1
  • 65
    • 0001281188 scopus 로고
    • Spreads and ovoids in finite generalized quadrangles
    • J. A. Thas and S. E. Payne, Spreads and ovoids in finite generalized quadrangles, Geometrica Dedicata, 52 (1994), 227-253.
    • (1994) Geometrica Dedicata , vol.52 , pp. 227-253
    • Thas, J.A.1    Payne, S.E.2
  • 67
    • 0001912075 scopus 로고    scopus 로고
    • Finding simple t-designs with enumeration techniques
    • A. Wasserman, Finding simple t-designs with enumeration techniques, J. Comb. Des. (2), 6 (1998), 79-90.
    • (1998) J. Comb. Des. , vol.6 , Issue.2 , pp. 79-90
    • Wasserman, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.