THE ELECTRONIC JOURNAL OF COMBINATORICS 4 (1997), DS #5.

Venn Diagram Survey
References

References to Venn Diagrams

  1. [AC] Daniel E. Anderson and Frank L. Cleaver, Venn-type diagrams for arguments of n terms, J. Symbolic Logic, 30 (1965) 113-118.
  2. [An] J. Anusiak, On Set-theoretically Independent Collections of Balls, Colloquium Mathematicum, 13 (1965) 223-233.
  3. [Ba] Margaret E. Baron, A Note on the historical development of logic diagrams: Leibniz, Euler, and Venn, Mathematical Gazette, 52 (1969) 113-125.
  4. [Be] E.C. Berkeley, Boolean algebra (the technique for manipulating "and", "or", "not" and conditions) and applications to insurance, The Record, American Institute of Actuaries, 26 (1937) 373-414. [According to [Grün75], this paper contains a general Venn diagram construction].
  5. [Boy] A.V. Boyd, Venn diagram of rectangles, Mathematics Magazine, 58 (1985) 251.
  6. [Bow] L.J. Bowles, Logic diagrams for up to n classes, Mathematical Gazette, 55 (1971) 370-373.
  7. [CHP95] K.B. Chilakamarri, P. Hamburger, and R.E. Pippert, Venn diagrams: announcement of some new results, Geombinatorics, 4 (1995) 129-137.
  8. [CHP96] K.B. Chilakamarri, P. Hamburger, and R.E. Pippert, Hamilton Cycles in Planar Graphs and Venn Diagrams, Journal of Combinatorial Theory (Series B), 67 (1996) 296-303.
  9. [CHP97a] Kiran B. Chilakamarri, Peter Hamburger and Raymond E. Pippert, Simple Venn diagrams on five curves, manuscript, Indiana-Purdue University, Fort Wayne, 1997.
  10. [CHP96b] Kiran B. Chilakamarri, Peter Hamburger and Raymond E. Pippert, Venn diagrams and planar graphs, Geometriae Dedicata, 1996, to appear.
  11. [Ed89a] Anthony W. F. Edwards, Venn diagrams for many sets, Bulletin of the International Statistical Institute, 47th Session, Paris, 1989. Contributed papers, Book 1, 311-312.
  12. [Ed89b] Anthony W. F. Edwards, Venn diagrams for many sets, New Scientist, 7 January 1989, 51-56.
  13. [Ed92] Anthony W. F. Edwards, Rotatable Venn Diagrams, Mathematics Review 2 (February 1992) 19-21.
  14. [Ed96] Anthony W. F. Edwards, 7-set Venn diagrams with rotational and polar symmetry, Combinatorics, Probability, and Computing, to appear, 1997.
  15. [ES] Anthony W. F. Edwards and C.A.B. Smith, New 3-set Venn diagram, Nature, (Scientific Correspondence), 339 (1989) 263.
  16. [FKG] J. Chris Fisher, E. L. Koh, and Branko Grünbaum, Diagrams Venn and How, Mathematics Magazine, 61 (1988) 36-40.
  17. [Ga] Martin Gardner, Logic, Machines, and Diagrams, McGraw-Hill, New York, 1958.
  18. [GKP] Ronald Graham, Donald Knuth, and Oren Patashnik, Concrete Mathematics, Addison-Wesley, 1989. [Exercises about Venn diagrams (1.5 and 1.22) may be found on pages 17 and 20, with corresponding solutions on pages 483 and 486.]
  19. [Gr75] Branko Grünbaum, Venn diagrams and Independent Families of Sets, Mathematics Magazine, Jan-Feb 1975, 13-23. [Grünbaum awarded the MAA Lester R. Ford prize for this paper in 1976 (see AMM, Aug-Sept. 1976, pg. 587).]
  20. [Gr84a] Branko Grünbaum, The Construction of Venn Diagrams, The College Mathematics Journal, 15 (1984) 238-247.
  21. [Gr84b] Branko Grünbaum, On Venn Diagrams and the Counting of Regions, The College Mathematics Journal, 15 (1984) 433-435.
  22. [Gr92a] Branko Grünbaum, Venn Diagrams I, Geombinatorics, Volume I, Issue 4, (1992) 5-12.
  23. [Gr92b] Branko Grünbaum, Venn Diagrams II, Geombinatorics, Volume II, Issue 2, (1992) 25-32.
  24. [GW] Branko Grünbaum and Peter Winkler, A Venn Diagram of 5 Triangles, Mathematics Magazine, 55 (1982) 311.
  25. [HP96a] P. Hamburger and R.E. Pippert, Venn said it couldn't be done, American Scientist, 1996, to appear.
  26. [HP96c] P. Hamburger and R.E. Pippert, Simple, reducible Venn diagrams on five curves and Hamiltonian cycles, Geometriae Dedicata, 1996, to appear.
  27. [He] D. W. Henderson, Venn diagrams for more than four classes, American Mathematical Monthly, 70 (1963) 424-426.
  28. [JP] D.S. Johnson and H.O. Pollack, Hypergraph Planarity and the Complexity of Drawing Venn Diagrams, Journal of Graph Theory, 11 (1987). [Earlier version appears in Colloquim on the Theory of Algorithms, North-Holland, 1985.]
  29. [Mo] T. Moor, Jr. On the construction of Venn diagrams, J. Symbolic Logic, 24 (1959) 303-304.
  30. [No] P. Nowicki, Koniczynko n-listna, [In Polish], Wiadom. Mat., 19 (1975) 11-18.
  31. [RRS] A. Rényi, V. Rényi, and J. Surányi, Sur l'indépendance des Domaines Simples dans l'espace Euclidien a n dimensions, Colloquium Mathematicum, 2 (1951) 130-135. [Come erroneous statements made in this paper are corrected in [Gr75]]
  32. [Sc] A. J. Schwenk, Venn diagram for five sets, Mathematics Magazine, 57 (1984) 297.
  33. [Ve80] J. Venn, On the diagrammatic and mechanical representation of propositions and reasonings, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 9 (1880) 1-18.
  34. [Ve81] J. Venn, Symbolic Logic, MacMillan, London 1881, 2nd ed., 1894.
  35. [We] B. Weglorz, Nerves and Set-theoretical Independence, Colloquium Mathimaticum, 13 (1964) 17-19.
  36. [Wi] Peter Winkler, Venn diagrams: Some observations and an open problem, Congressus Numerantium, 45 (1984) 267-274.
  37. Obscure references (and not necessarily relevant).

    Other References Used

  38. [BS] G.S. Bhat and C.D.Savage, Balanced Gray Codes, Electronic Journal of Combinatorics, Volume 3 (no. 1), #R25.
  39. [Or] O. Ore, The Four-Color Problem, Academic Press, New York, London, 1967.
  40. [St] Ian Stewart, Game, Set, and Math, Basil Blackwell, 1989.
  41. [Wh] H. Whitney, A Theorem on Graphs, Annals of Math., 32 (1931) 378-390.

    Off-site references

    The external sites listed below are not endorsed by The Electronic Journal of Combinatorics and do not form part of this article.

  42. [COS] The set partitions information page, part of the Combinatorial Object Server.
  43. [MAC] The MacTutor History of Mathematics Archive contains a short biography of John Venn.
  44. [GC] The Geometry Center at the University of Minnesota.
  45. [KP] Robert Scharein's KnotPlot site.

THE ELECTRONIC JOURNAL OF COMBINATORICS 4 (1997), DS #5.