1998 年度実績報告書

幾何的組合せ構造の研究

研究課題

研究課題/領域番号	09640290
研究機関	慶応義塾大学
研究代表者	太田克弘慶應義塾大学, 理工学部, 助教授 (40213722)
研究分担者	徳重典英琉球大学, 教育学部, 助教授 (00217481) 松本眞慶應義塾大学, 理工学部, 助教授 (70231602) 前田吉昭慶應義塾大学, 理工学部, 教授 (40101076) 榎本彦衛慶應義塾大学, 理工学部, 教授 (00011669) 塩川宇賢慶應義塾大学, 理工学部, 教授 (00015835)
キーワード	三角形分割 / 四角形分割 / cycle parity / 写像類群 / 本型空間
研究概要	閉曲面上の三角形分割や四角形分割は、そのメッシュを十分細かくすることでその閉曲面を離散的に近似していると考えることができる。同じ頂点数の三角形分割や四角形分割に限っても非常にたくさん存在するが、まずそれらが互いに対角変形と呼ばれる局所的な変形の繰り返しで互いに移り合えるかどうかについての研究を行った。結果として、三角形分割については、十分頂点数が大きければ、すなわちそのグラフが閉曲面を十分よく近似していれば、互いに移り合うことが示された。一方、四角形分割においては、cycle parityと呼ばれる離散的不変量が存在し、それが閉曲面の写像類群の構造と深い関係にあることを示した。閉曲面に埋め込まれたグラフにおける頂点の次数は、その点における曲面の曲率を離散化したものとみなせる。球面上に埋め込まれた3連結グラフにおいて、指定した大きさの連結部分集合で、どの程度次数和の小さいものが存在するか、すなわちどの程度曲率の大きい部分構造があるかについての研究を行った。また、木型空間へグラフを埋め込む問題においては、まず辺が本の背と跨ってはいけないという制約のもとに、完全2部グラフが何ページの木型空間に埋め込めるか、という未解決問題に関して、既存の評価よりよい評価を得ることに成功した。一般のグラフについては、本の背と辺との交差数の下限の評価を与えた。その他、トポロジーにおける写像類群のアルティン群による表示、基本群へのガロア作用、整数論をもちいたDifference setの研究、既約多項式の探索、単体の等距離埋め込み問題、グラフを平面上の整数距離グラフとして埋め込む問題などについて研究した。

研究成果

(40件)

すべてその他

すべて文献書誌 (40件)

[文献書誌] H.Enomoto,et al.: "Long Cycles Passing Through a Specified Edge in a 3-Connected graph" Journal of Graph Theory. 24. 275-279 (1997)
[文献書誌] A.Nakamoto,et al.: "Diagonal Transformations in Quadrangulations and Dehn Twists Preserving Cycle Parities" Journal of Combinatorial Theory Ser.B. 69. 125-141 (1997)
[文献書誌] A.Nakamoto,et al.: "Three-Cycle Reversions in Oriented Planar Triangulations" Yokohama Mathematical Journal. 44. 123-139 (1997)
[文献書誌] A.Nakamoto,et al.: "Diagonal Transformations of Graphs and Dehn Twists of Surfaces" Journal of Combinatorial Theory Ser.B. 70. 292-300 (1997)
[文献書誌] H.Enomoto,et al.: "On the Pagenumber of Complete Bipartite Graphs" Journal of Combinatorial Theory Ser.B. 71. 290-299 (1997)
[文献書誌] H.Maehara,et al.: "Every Graph Is an Integral Distance Graph in the Plane" Journal of Combinatorial Theory Ser.A. 80. 290-294 (1997)
[文献書誌] P.Frankl,et al.: "Uniform intersecting families with covering number restrictions" Combinatorics,Probablity & Computing. 7. 47-56 (1998)
[文献書誌] H.Enomoto,et al.: "A Lower Bound for the Number of Edge-Crossings over the Spine of the Book Embedding of Graphs" to appear in Discrete Applied Mathematics.
[文献書誌] Y.Egawa,et al.: "Vertex-Disjoint Claws in Graphs" to appear in Discrete Mathematics.
[文献書誌] H.Enomoto,et al.: "Connected Subgraphs with Small Degree Sums in 3-Connected Planar Graphs" to appear in Journal of Graph Theory.
[文献書誌] H.Enomoto,et al.: "Pyramidal Tours with Step-backs and the Asymmetric Traveling Salesman Problem" to appear in Discrete Applied Mathematics.
[文献書誌] Y.Nakai,et al.: "Normality of numbers generated by values of polynomials at prime" Acta Arith.LXXXI4. 345-346 (1997)
[文献書誌] D.Duverney,et al.: "Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers" Proc.Japan Acad.Sci.73A. 140-142 (1997)
[文献書誌] D.Duverney,et al.: "On some arithmetical properties of Rogers-Ramanujan continued fraction" to appear in Osaka J.Math.
[文献書誌] H.Enomoto,et al.: "Graph decompositions without isolated vertices.II" J.Math.Soc.Japan. 49. 161-180 (1997)
[文献書誌] H.Enomoto,et al.: "Graph decompositions without isolated vertices.III" J.Graph Theory. 24. 155-164 (1997)
[文献書誌] H.Enomoto: "Toughness and existence of k-factors.III" Discrete Mathematics. 189. 277-282 (1998)
[文献書誌] H.Enomoto,et al.: "A note on difference sets" J.Combinatorial Theory Ser.A. 84. 133-144 (1998)
[文献書誌] H.Enomoto,et al.: "Super edge-magic graphs" SUT Journal of Mathematics. 34. 105-109 (1998)
[文献書誌] H.Enomoto: "On the existence of disjoint cycles in a graph" to appear in Combinatorica.
[文献書誌] H.Enomoto,et al.: "Induced graph theorem on magic valuations" to appear in Ars Combinatoria.
[文献書誌] Y.Maeda,et al.: "Minimal orbits of metrics" Journal of Geometry and Physics. 23. 319-349 (1997)
[文献書誌] H.Kozono,et al.: "A Yang-Mills-Higgs gradient flow on \{〓bfR}^3\ blowing up at infinity" Proceedings of the Japan Academy. 74A. 71-73 (1998)
[文献書誌] H.Omori,et al.: "Poincare-Cartan class and deformation quantization of Kaehler manifolds" Communications in Mathematical Physics. 194. 207-230 (1998)
[文献書誌] H.Omori,et al.: "Noncommutative 3-sphere;A model of noncommutative contact algebras" Journal of Mathematical Society of Japan. 50. 915-943 (1998)
[文献書誌] H.Omori,et al.: "Deformation quantization of the Poisson algebra of Laurant polynomials" to appear in Letters in Mathematical Physics.
[文献書誌] T.Anazawa,et al.: "An explicit solution of optimum requirement spanning tree with maximum degree conditions" Congressus Numerantium. 117. 43-52 (1997)
[文献書誌] M.Genma,et al.: "Cyclic resolvability of cyclic Steiner 2-designs" Journal of Combinatorial Designs. 5. 177-187 (1997)
[文献書誌] M.Mishima,et al.: "Some types of cyclically resolvable cyclic Steiner 2-designs" Congressus Numerantium. 123. 193-203 (1997)
[文献書誌] M.Mishima,et al.: "Constructions of nested directed BIB designs" The Australasian Journal of Combinatorics. 18. 157-172 (1998)
[文献書誌] M.Mishima,et al.: "On the optimality of orthogonal arrays for correlated errors" to appear in Journal of Statistical Inference and Planning.
[文献書誌] T.Hishida,et al.: "Possible patterns of cyclic resolution of the BIB design associated with PG(7,2)" to appear in Congressus Numerantium.
[文献書誌] M.Matsumoto: "Simple cellular automata as pseudorandom m-sequence generators for built-in self-test" ACM Transactions on Modeling and Computer Simulation. 8. 31-42 (1998)
[文献書誌] M.Matsumoto,et al.: "Mersenne Twister:a 623-dimensionally equidistributed uniform pseudorandom number generator" ACM Transactions on Modeling and Computer Simulation. 8. 3-30 (1998)
[文献書誌] H.Ashihara,et al.: "An Application of Finite Projective Space to Replicated Data Management" to appear in Computer Systems Science & Engineering.
[文献書誌] F.Jaeger,et al.: "Association schemes related with type II matrices and spin models" Journal of Algebraic Combinatorics. 8. 39-72 (1998)
[文献書誌] H.Maehara,et al.: "Is there a circle that passes through a given number of lattice points?" European Journal of Combinatorics. 19. 591-592 (1998)
[文献書誌] T.Kumada,et al.: "New primitive t-nomials(t=3,5)over GF(2)whose degree is a Mersenne exponent" to appear in Mathematics of Computation.
[文献書誌] P.Frankl,et al.: "Some inequalities concerning cross-intersecting families" Combinatorics,Probability & Computing. 7. 247-260 (1998)
[文献書誌] P.Frankl,et al.: "Erdos-Ko-Rado theorem for integer sequences" to appear in Combinatorica.

1998 年度 実績報告書

幾何的組合せ構造の研究

研究代表者

太田 克弘 慶應義塾大学, 理工学部, 助教授 (40213722)

研究成果

[文献書誌] H.Enomoto,et al.: "Long Cycles Passing Through a Specified Edge in a 3-Connected graph" Journal of Graph Theory. 24. 275-279 (1997)

[文献書誌] A.Nakamoto,et al.: "Diagonal Transformations in Quadrangulations and Dehn Twists Preserving Cycle Parities" Journal of Combinatorial Theory Ser.B. 69. 125-141 (1997)

[文献書誌] A.Nakamoto,et al.: "Three-Cycle Reversions in Oriented Planar Triangulations" Yokohama Mathematical Journal. 44. 123-139 (1997)

[文献書誌] A.Nakamoto,et al.: "Diagonal Transformations of Graphs and Dehn Twists of Surfaces" Journal of Combinatorial Theory Ser.B. 70. 292-300 (1997)

[文献書誌] H.Enomoto,et al.: "On the Pagenumber of Complete Bipartite Graphs" Journal of Combinatorial Theory Ser.B. 71. 290-299 (1997)

[文献書誌] H.Maehara,et al.: "Every Graph Is an Integral Distance Graph in the Plane" Journal of Combinatorial Theory Ser.A. 80. 290-294 (1997)

[文献書誌] P.Frankl,et al.: "Uniform intersecting families with covering number restrictions" Combinatorics,Probablity & Computing. 7. 47-56 (1998)

[文献書誌] H.Enomoto,et al.: "A Lower Bound for the Number of Edge-Crossings over the Spine of the Book Embedding of Graphs" to appear in Discrete Applied Mathematics.

[文献書誌] Y.Egawa,et al.: "Vertex-Disjoint Claws in Graphs" to appear in Discrete Mathematics.

[文献書誌] H.Enomoto,et al.: "Connected Subgraphs with Small Degree Sums in 3-Connected Planar Graphs" to appear in Journal of Graph Theory.

[文献書誌] H.Enomoto,et al.: "Pyramidal Tours with Step-backs and the Asymmetric Traveling Salesman Problem" to appear in Discrete Applied Mathematics.

[文献書誌] Y.Nakai,et al.: "Normality of numbers generated by values of polynomials at prime" Acta Arith.LXXXI4. 345-346 (1997)

[文献書誌] D.Duverney,et al.: "Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers" Proc.Japan Acad.Sci.73A. 140-142 (1997)

[文献書誌] D.Duverney,et al.: "On some arithmetical properties of Rogers-Ramanujan continued fraction" to appear in Osaka J.Math.

[文献書誌] H.Enomoto,et al.: "Graph decompositions without isolated vertices.II" J.Math.Soc.Japan. 49. 161-180 (1997)

[文献書誌] H.Enomoto,et al.: "Graph decompositions without isolated vertices.III" J.Graph Theory. 24. 155-164 (1997)

[文献書誌] H.Enomoto: "Toughness and existence of k-factors.III" Discrete Mathematics. 189. 277-282 (1998)

[文献書誌] H.Enomoto,et al.: "A note on difference sets" J.Combinatorial Theory Ser.A. 84. 133-144 (1998)

[文献書誌] H.Enomoto,et al.: "Super edge-magic graphs" SUT Journal of Mathematics. 34. 105-109 (1998)

[文献書誌] H.Enomoto: "On the existence of disjoint cycles in a graph" to appear in Combinatorica.

[文献書誌] H.Enomoto,et al.: "Induced graph theorem on magic valuations" to appear in Ars Combinatoria.

[文献書誌] Y.Maeda,et al.: "Minimal orbits of metrics" Journal of Geometry and Physics. 23. 319-349 (1997)

[文献書誌] H.Kozono,et al.: "A Yang-Mills-Higgs gradient flow on \{〓bfR}^3\ blowing up at infinity" Proceedings of the Japan Academy. 74A. 71-73 (1998)

[文献書誌] H.Omori,et al.: "Poincare-Cartan class and deformation quantization of Kaehler manifolds" Communications in Mathematical Physics. 194. 207-230 (1998)

[文献書誌] H.Omori,et al.: "Noncommutative 3-sphere;A model of noncommutative contact algebras" Journal of Mathematical Society of Japan. 50. 915-943 (1998)

[文献書誌] H.Omori,et al.: "Deformation quantization of the Poisson algebra of Laurant polynomials" to appear in Letters in Mathematical Physics.

[文献書誌] T.Anazawa,et al.: "An explicit solution of optimum requirement spanning tree with maximum degree conditions" Congressus Numerantium. 117. 43-52 (1997)

[文献書誌] M.Genma,et al.: "Cyclic resolvability of cyclic Steiner 2-designs" Journal of Combinatorial Designs. 5. 177-187 (1997)

[文献書誌] M.Mishima,et al.: "Some types of cyclically resolvable cyclic Steiner 2-designs" Congressus Numerantium. 123. 193-203 (1997)

[文献書誌] M.Mishima,et al.: "Constructions of nested directed BIB designs" The Australasian Journal of Combinatorics. 18. 157-172 (1998)

[文献書誌] M.Mishima,et al.: "On the optimality of orthogonal arrays for correlated errors" to appear in Journal of Statistical Inference and Planning.

[文献書誌] T.Hishida,et al.: "Possible patterns of cyclic resolution of the BIB design associated with PG(7,2)" to appear in Congressus Numerantium.

[文献書誌] M.Matsumoto: "Simple cellular automata as pseudorandom m-sequence generators for built-in self-test" ACM Transactions on Modeling and Computer Simulation. 8. 31-42 (1998)

[文献書誌] M.Matsumoto,et al.: "Mersenne Twister:a 623-dimensionally equidistributed uniform pseudorandom number generator" ACM Transactions on Modeling and Computer Simulation. 8. 3-30 (1998)

[文献書誌] H.Ashihara,et al.: "An Application of Finite Projective Space to Replicated Data Management" to appear in Computer Systems Science & Engineering.

[文献書誌] F.Jaeger,et al.: "Association schemes related with type II matrices and spin models" Journal of Algebraic Combinatorics. 8. 39-72 (1998)

[文献書誌] H.Maehara,et al.: "Is there a circle that passes through a given number of lattice points?" European Journal of Combinatorics. 19. 591-592 (1998)

[文献書誌] T.Kumada,et al.: "New primitive t-nomials(t=3,5)over GF(2)whose degree is a Mersenne exponent" to appear in Mathematics of Computation.

[文献書誌] P.Frankl,et al.: "Some inequalities concerning cross-intersecting families" Combinatorics,Probability & Computing. 7. 247-260 (1998)

[文献書誌] P.Frankl,et al.: "Erdos-Ko-Rado theorem for integer sequences" to appear in Combinatorica.

1998 年度実績報告書

太田克弘慶應義塾大学, 理工学部, 助教授 (40213722)