The Resource Combinatorial games : tic-tac-toe theory, József Beck

Combinatorial games : tic-tac-toe theory, József Beck

Label
Combinatorial games : tic-tac-toe theory
Title
Combinatorial games
Title remainder
tic-tac-toe theory
Statement of responsibility
József Beck
Creator
Subject
Language
eng
Member of
Cataloging source
UKM
http://library.link/vocab/creatorName
Beck, József
Dewey number
519.3
Illustrations
illustrations
Index
no index present
LC call number
QA269
LC item number
.B335 2008
Literary form
non fiction
Nature of contents
bibliography
Series statement
Encyclopedia of mathematics and its applications
Series volume
v. 114
http://library.link/vocab/subjectName
  • Game theory
  • Combinatorial analysis
  • Théorie des jeux
  • Analyse combinatoire
Label
Combinatorial games : tic-tac-toe theory, József Beck
Instantiates
Publication
Bibliography note
Includes bibliographical references
Contents
  • pt. A. Weak win and strong draw -- ch. I. Win vs. weak win -- Illustration : every finite point set in the plane is a weak winner -- Analyzing the proof of theorem 1.1 -- Examples : tic-tac-toe games -- More examples : tic-tac-toe like games -- Games on hypergraphs, and the combinatorial chaos -- ch. II. The main result : exact solutions for infinite classes of games -- Ramsey theory and clique games -- Arithmetic progressions -- Two-dimensional arithmetic progressions -- Explaining the exact solutions : a meta-conjecture -- Potentials and the Erdős-Selfridge theorem -- Local vs. global -- Ramsey theory and hypercube tic-tac-toe -- pt. B. Basic potential technique : game-theoretic first and second moments -- ch. III. Simple applications -- Easy building via theorem 1.2 -- Games beyond Ramsey theory -- A generalization of Kaplansky's game -- ch. IV. Games and randomness -- Discrepancy games and the variance -- Biased discrepancy games : when the extension from fair to biased works! -- A simple illustration of "randomness" (I) -- A simple illustration of "randomness" (II) -- Another illustration of "randomness" in games --
  • pt. C. Advanced weak win : game-theoretic higher moment -- ch. V. Self-improving potentials -- Motivating the probabilistic approach -- Game-theoretic second moment : application to the picker-choose game -- Weak win in the lattice games -- Game-theoretic higher moments -- Exact solution of the clique game (I) -- More applications -- Who-scores-more games -- ch. VI. What is the biased meta-conjecture, and why is it so difficult? -- Discrepancy games (I) -- Discrepancy games (II) -- Biased games (I) : biased meta-conjecture -- Biased games (II) : sacrificing the probabilistic intuition to force negativity -- Biased games (III) : sporadic results -- Biased games (IV) : more sporadic results -- pt. D. Advanced strong draw : game-theoretic independence -- ch. VII. BigGame-SmallGame decomposition -- The Hales-Jewett conjecture -- Reinforcing the Erdős-Selfridge technique (I) -- Reinforcing the Erdős-Selfridge technique (II) -- Almost disjoint hypergraphs -- Exact solution of the clique game (II) --
  • ch. VIII. Advanced decomposition -- Proof of the second ugly theorem -- Breaking the "square-root barrier" (I) -- Breaking the "square-root barrier" (II) -- Van der Waerden game and the RELARIN technique -- ch. IX. Game-theoretic lattice-numbers -- Winning planes : exact solution -- Winning lattices : exact solution -- I-can-you-can't games - second player's moral victory -- ch. X. Conclusion -- More exact solutions and more partial results -- Miscellany (I) -- Miscellany (II) -- Concluding remarks -- Appendix A : Ramsey numbers -- Appendix B : Hales-Jewett theorem : Shelah's proof -- Appendix C : A formal treatment of positional games -- Appendix D : An informal introduction to game theory
Dimensions
24 cm.
Extent
xiv, 732 p.
Isbn
9780521461009
Isbn Type
(hbk.)
Lccn
2008275067
Other physical details
ill.
System control number
  • (CaMWU)u2136444-01umb_inst
  • 2215735
  • (Sirsi) i9780521461009
  • (OCoLC)175284055
Label
Combinatorial games : tic-tac-toe theory, József Beck
Publication
Bibliography note
Includes bibliographical references
Contents
  • pt. A. Weak win and strong draw -- ch. I. Win vs. weak win -- Illustration : every finite point set in the plane is a weak winner -- Analyzing the proof of theorem 1.1 -- Examples : tic-tac-toe games -- More examples : tic-tac-toe like games -- Games on hypergraphs, and the combinatorial chaos -- ch. II. The main result : exact solutions for infinite classes of games -- Ramsey theory and clique games -- Arithmetic progressions -- Two-dimensional arithmetic progressions -- Explaining the exact solutions : a meta-conjecture -- Potentials and the Erdős-Selfridge theorem -- Local vs. global -- Ramsey theory and hypercube tic-tac-toe -- pt. B. Basic potential technique : game-theoretic first and second moments -- ch. III. Simple applications -- Easy building via theorem 1.2 -- Games beyond Ramsey theory -- A generalization of Kaplansky's game -- ch. IV. Games and randomness -- Discrepancy games and the variance -- Biased discrepancy games : when the extension from fair to biased works! -- A simple illustration of "randomness" (I) -- A simple illustration of "randomness" (II) -- Another illustration of "randomness" in games --
  • pt. C. Advanced weak win : game-theoretic higher moment -- ch. V. Self-improving potentials -- Motivating the probabilistic approach -- Game-theoretic second moment : application to the picker-choose game -- Weak win in the lattice games -- Game-theoretic higher moments -- Exact solution of the clique game (I) -- More applications -- Who-scores-more games -- ch. VI. What is the biased meta-conjecture, and why is it so difficult? -- Discrepancy games (I) -- Discrepancy games (II) -- Biased games (I) : biased meta-conjecture -- Biased games (II) : sacrificing the probabilistic intuition to force negativity -- Biased games (III) : sporadic results -- Biased games (IV) : more sporadic results -- pt. D. Advanced strong draw : game-theoretic independence -- ch. VII. BigGame-SmallGame decomposition -- The Hales-Jewett conjecture -- Reinforcing the Erdős-Selfridge technique (I) -- Reinforcing the Erdős-Selfridge technique (II) -- Almost disjoint hypergraphs -- Exact solution of the clique game (II) --
  • ch. VIII. Advanced decomposition -- Proof of the second ugly theorem -- Breaking the "square-root barrier" (I) -- Breaking the "square-root barrier" (II) -- Van der Waerden game and the RELARIN technique -- ch. IX. Game-theoretic lattice-numbers -- Winning planes : exact solution -- Winning lattices : exact solution -- I-can-you-can't games - second player's moral victory -- ch. X. Conclusion -- More exact solutions and more partial results -- Miscellany (I) -- Miscellany (II) -- Concluding remarks -- Appendix A : Ramsey numbers -- Appendix B : Hales-Jewett theorem : Shelah's proof -- Appendix C : A formal treatment of positional games -- Appendix D : An informal introduction to game theory
Dimensions
24 cm.
Extent
xiv, 732 p.
Isbn
9780521461009
Isbn Type
(hbk.)
Lccn
2008275067
Other physical details
ill.
System control number
  • (CaMWU)u2136444-01umb_inst
  • 2215735
  • (Sirsi) i9780521461009
  • (OCoLC)175284055

Library Locations

  • Albert D. Cohen Management LibraryBorrow it
    181 Freedman Crescent, Winnipeg, MB, R3T 5V4, CA
    49.807878 -97.129961
  • Architecture/Fine Arts LibraryBorrow it
    84 Curry Place, Winnipeg, MB, CA
    49.807716 -97.136226
  • Archives and Special CollectionsBorrow it
    25 Chancellors Circle (Elizabeth Dafoe Library), Room 330, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Bibliothèque Alfred-Monnin (Université de Saint-Boniface)Borrow it
    200, avenue de la Cathédrale, Local 2110, Winnipeg, MB, R2H 0H7, CA
    49.888861 -97.119735
  • Bill Larson Library (Grace Hospital)Borrow it
    300 Booth Drive, G-227, Winnipeg, MB, R3J 3M7, CA
    49.882400 -97.276436
  • Carolyn Sifton - Helene Fuld Library (St. Boniface General Hospital)Borrow it
    409 Tache Avenue, Winnipeg, MB, R2H 2A6, CA
    49.883388 -97.126050
  • Concordia Hospital LibraryBorrow it
    1095 Concordia Avenue, Winnipeg, MB, R2K 3S8, CA
    49.913252 -97.064683
  • Donald W. Craik Engineering LibraryBorrow it
    75B Chancellors Circle (Engineering Building E3), Room 361, Winnipeg, MB, R3T 2N2, CA
    49.809053 -97.133292
  • E.K. Williams Law LibraryBorrow it
    224 Dysart Road, Winnipeg, MB, R3T 5V4, CA
    49.811829 -97.131017
  • Eckhardt-Gramatté Music LibraryBorrow it
    136 Dafoe Road (Taché Arts Complex), Room 257, Winnipeg, MB, R3T 2N2, CA
    49.807964 -97.132222
  • Elizabeth Dafoe LibraryBorrow it
    25 Chancellors Circle, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Fr. H. Drake Library (St. Paul's College)Borrow it
    70 Dysart Road, Winnipeg, MB, R3T 2M6, CA
    49.810605 -97.138184
  • J.W. Crane Memorial Library (Deer Lodge Centre)Borrow it
    2109 Portage Avenue, Winnipeg, MB, R3J 0L3, CA
    49.878000 -97.235520
  • Libraries Annex (not open to the public; please see web page for details)Borrow it
    25 Chancellors Circle (in the Elizabeth Dafoe Library), Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Neil John Maclean Health Sciences LibraryBorrow it
    727 McDermot Avenue (Brodie Centre), 200 Level, Winnipeg, MB, R3E 3P5, CA
    49.903563 -97.160554
  • Sciences and Technology LibraryBorrow it
    186 Dysart Road, Winnipeg, MB, R3T 2M8, CA
    49.811526 -97.133257
  • Seven Oaks General Hospital LibraryBorrow it
    2300 McPhillips Street, Winnipeg, MB, R2V 3M3, CA
    49.955177 -97.148865
  • Sister St. Odilon Library (Misericordia Health Centre)Borrow it
    99 Cornish Avenue, Winnipeg, MB, R3C 1A2, CA
    49.879592 -97.160425
  • St. John's College LibraryBorrow it
    92 Dysart Road, Winnipeg, MB, R3T 2M5, CA
    49.811242 -97.137156
  • Victoria General Hospital LibraryBorrow it
    2340 Pembina Highway, Winnipeg, MB, R3T 2E8, CA
    49.806755 -97.152739
  • William R Newman Library (Agriculture)Borrow it
    66 Dafoe Road, Winnipeg, MB, R3T 2R3, CA
    49.806936 -97.135525
Processing Feedback ...