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Combinatorics (book list)

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This is a section of the Basic Math Library List


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14. Combinatorics
      Combinatorial structures. Enumeration: exact and asymptotic. Graph theory. Probabilistic and extremal combinatorics. 
      Designs and finite geometries. Relations with linear algebra, representation theory and commutative algebra. 
      Topological and analytical techniques in combinatorics. Combinatorial geometry. Combinatorial number theory. 
      Polyhedral combinatorics and combinatorial optimization.
      Connections with sections  1, 2, 3, 4, 7, 10, 13, 15.



Discrete Mathematics

  • Albertson, Michael O. and Hutchinson, Joan P. Discrete Mathematics with Algorithms New York, NY: John Wiley, 1988.
  • Althoen, Steven C. and Bumcrot, Robert J. Introduction to Discrete Mathematics Boston, MA: PWS-Kent, 1988.
  • Biggs, Norman L. Discrete Mathematics, New York, NY: Clarendon Press, 1985, 1989. Revised Edition.
  • Bogart, Kenneth P. Discrete Mathematics Lexington, MA: D.C. Heath, 1988.

Doerr, Alan and Levasseur, Kenneth. Applied Discrete Structures for Computer Science Chicago, IL: Science Research Association, 1985.

Dossey, John A., et al. Discrete Mathematics Glenview, IL: Scott Foresman, 1986.

  • Epp, Susanna S. Discrete Mathematics with Applications Belmont, CA: Wadsworth, 1990.

Finkbeiner, Daniel T. and Lindstrom, Wendell D. A Primer of Discrete Mathematics New York, NY: W.H. Freeman, 1987.

  • Gerstein, Larry J. Discrete Mathematics and Algebraic Structures New York, NY: W.H. Freeman, 1987.

Grimaldi, Ralph P. Discrete and Combinatorial Mathematics: An Applied Introduction, Reading, MA: Addison-Wesley, 1989. Second Edition.

  • Johnsonbaugh, Richard. Discrete Mathematics, New York, NY: Macmillan, 1990. Second Edition.
    • Maurer, Stephen B. and Ralston, Anthony. Discrete Algorithmic Mathematics Reading, MA: Addison-Wesley, 1991.

McEliece, Robert J.; Ash, Robert B.; and Ash, Carol. Introduction to Discrete Mathematics Cambridge, MA: Random House, 1989.

Nicodemi, Olympia. Discrete Mathematics: A Bridge to Computer Science and Advanced Mathematics St.~Paul, MN: West, 1987.

Polimeni, Albert D. and Straight, H. Joseph. Foundations of Discrete Mathematics, Pacific Grove, CA: Brooks/Cole, 1985, 1990. Second Edition.

Prather, Ronald. Elements of Discrete Mathematics Boston, MA: Houghton Mifflin, 1986.

  • Roman, Steven. An Introduction to Discrete Mathematics, San Diego, CA: Harcourt Brace Jovanovich, 1989. Second Edition.

Rosen, Kenneth H. Discrete Mathematics and its Applications Cambridge, MA: Random House, 1988.

    • Ross, Kenneth A. and Wright, Charles R.B. Discrete Mathematics, Englewood Cliffs, NJ: Prentice Hall, 1985, 1988. Second Edition.


Finite Mathematics

  • Anton, Howard; Kolman, Bernard; and Averbach, Bonnie. Applied Finite Mathematics, New York, NY: Academic Press, 1982, 1988. Fourth Edition.
  • Bittinger, Marvin L. and Crown, J. Conrad. Finite Mathematics Reading, MA: Addison-Wesley, 1989.

Cozzens, Margaret B. and Porter, Richard D. Mathematics and Its Applications to Management, Life, and Social Sciences With Finite and Discrete Mathematics Lexington, MA: D.C. Heath, 1987.

  • Davis, Morton D. The Art of Decision-Making New York, NY: Springer-Verlag, 1986.

Farlow, Stanley J. and Haggard, Gary M. Finite Mathematics and Its Applications Cambridge, MA: Random House, 1988.

    • Goldstein, Larry J.; Schneider, David I.; and Siegel, Martha J. Finite Mathematics and Its Applications, Englewood Cliffs, NJ: Prentice Hall, 1984, 1991. Fourth Edition.

Hoenig, Alan. Applied Finite Mathematics New York, NY: McGraw-Hill, 1990.

      • Kemeny, John G.; Snell, J. Laurie; and Thompson, Gerald L. Introduction to Finite Mathematics, Englewood Cliffs, NJ: Prentice Hall, 1974. Third Edition.
  • Maki, Daniel P. and Thompson, Maynard. Finite Mathematics, New York, NY: McGraw-Hill, 1978, 1989. Third Edition.

Malkevitch, Joseph and Meyer, Walter. Graphs, Models, and Finite Mathematics Englewood Cliffs, NJ: Prentice Hall, 1974.

Smith, Karl J. Finite Mathematics, Pacific Grove, CA: Brooks/Cole, 1988. Second Edition.

Spence, Lawrence E.; Vanden Eynden, Charles; and Gallin, Daniel. Finite Mathematics Glenview, IL: Scott Foresman, 1990.

  • Tan, S.T. Applied Finite Mathematics, Boston, MA: Prindle, Weber and Schmidt, 1983, 1990. Third Edition.


Introductory Combinatorics

  • Anderson, Ian. A First Course in Combinatorial Mathematics New York, NY: Oxford University Press, 1974.

Berge, Claude. Principles of Combinatorics New York, NY: Academic Press, 1971.

Bogart, Kenneth P. Introductory Combinatorics, San Diego, CA: Harcourt Brace Jovanovich, 1990. Second Edition.

Bose, R.C. and Manvel, B. Introduction to Combinatorial Theory New York, NY: John Wiley, 1984.

    • Brualdi, Richard A. Introductory Combinatorics, Amsterdam: North-Holland, 1977, 1991. Second Edition.
  • Cohen, Daniel I.A. Basic Techniques of Combinatorial Theory New York, NY: John Wiley, 1978.
      • Graham, Ronald L.; Knuth, Donald E.; and Patashnik, Oren. Concrete Mathematics: A Foundation for Computer Science Reading, MA: Addison-Wesley, 1989.
  • Hillman, Abraham P.; Alexanderson, Gerald L.; and Grassl, Richard M. Discrete and Combinatorial Mathematics San Francisco, CA: Dellen, 1987.

Jackson, Brad and Thoro, Dmitri. Applied Combinatorics with Problem Solving Reading, MA: Addison-Wesley, 1990.

  • Liu, C.L. Introduction to Applied Combinatorial Mathematics New York, NY: McGraw-Hill, 1968.
      • Niven, Ivan M. Mathematics of Choice or How to Count Without Counting Washington, DC: Mathematical Association of America, 1975.

Page, E.S. and Wilson, L.B. An Introduction to Computational Combinatorics New York, NY: Cambridge University Press, 1979.

    • Roberts, Fred S. Applied Combinatorics Englewood Cliffs, NJ: Prentice Hall, 1984.
    • Stanton, Dennis and White, Dennis. Constructive Combinatorics New York, NY: Springer-Verlag, 1986.
    • Tucker, Alan. Applied Combinatorics New York, NY: John Wiley, 1980, 1984.


Advanced Combinatorics

Aigner, Martin. Combinatorial Search New York, NY: John Wiley, 1988.

Aigner, Martin. Combinatorial Theory New York, NY: Springer-Verlag, 1979.

    • Anderson, Ian. Combinatorics of Finite Sets New York, NY: Oxford University Press, 1987.
  • Anderson, Ian. Combinatorial Designs: Construction Methods New York, NY: Ellis Horwood, 1990.

Bollobas, Bela. Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability New York, NY: Cambridge University Press, 1986.

Brualdi, Richard A. and Ryser, H.J. Combinatorial Matrix Theory New York, NY: Cambridge University Press, 1991.

    • Conway, John Horton. On Numbers and Games New York, NY: Academic Press, 1976.
  • Denes, J. and Keedwell, A.D. Latin Squares and Their Applications New York, NY: Academic Press, 1974.
  • Erd os, P. and Spencer, Joel H. Probability Methods in Combinatorics New York, NY: Academic Press, 1974.

Goulden, I.P. and Jackson, D.M. Combinatorial Enumeration New York, NY: John Wiley, 1983.

    • Graham, Ronald L.; Rothschild, Bruce L.; and Spencer, Joel H. Ramsey Theory, New York, NY: John Wiley, 1980, 1990. Second Edition.

Greene, Daniel H. and Knuth, Donald E. Mathematics for the Analysis of Algorithms, New York, NY: Birkhauser, 1981, 1990. Third Edition.

Gusfield, Dan and Irving, Robert W. The Stable Marriage Problem: Structure and Algorithms Cambridge, MA: MIT Press, 1989.

  • Hall, Marshall, Jr. Combinatorial Theory, New York, NY: John Wiley, 1986. Second Edition.
      • Lovasz, Laszlo. Combinatorial Problems and Exercises Amsterdam: North-Holland, 1979.

Lovasz, Laszlo. An Algorithmic Theory of Numbers, Graphs, and Convexity Philadelphia, PA: Society for Industrial and Applied Mathematics, 1986.

Polya, George and Read, Ronald C. Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds New York, NY: Springer-Verlag, 1987.

Polya, George; Tarjan, Robert E.; and Woods, Donald R. Notes on Introductory Combinatorics New York, NY: Birkhauser, 1983.

Ray-Chaudhuri, D.K., ed. Relations Between Combinatorics and Other Parts of Mathematics Providence, RI: American Mathematical Society, 1979.

Riordan, John. Combinatorial Identities New York, NY: John Wiley, 1968.

Riordan, John. An Introduction to Combinatorial Analysis Princeton, NJ: Princeton University Press, 1978.

Rota, Gian-Carlo, ed. Studies in Combinatorics Washington, DC: Mathematical Association of America, 1978.

      • Ryser, H.J. Combinatorial Mathematics Washington, DC: Mathematical Association of America, 1963.
    • Stanley, Richard P. Enumerative Combinatorics, Belmont, CA: Wadsworth, 1986.
  • Street, Anne P. and Street, Deborah J. Combinatorics of Experimental Design New York, NY: Clarendon Press, 1987.

Tomescu, Ioan. Problems in Combinatorics and Graph Theory New York, NY: John Wiley, 1985.

  • Vilenkin, N. Ya. Combinatorics New York, NY: Academic Press, 1971.

Wallis, W.D. Combinatorial Designs New York, NY: Marcel Dekker, 1988.


Graph Theory

Barnette, David. Map Coloring, Polyhedra, and the Four-Color Problem Washington, DC: Mathematical Association of America, 1983.

Beineke, Lowell W. and Wilson, Robin J., eds. Selected Topics in Graph Theory, New York, NY: Academic Press, 1978--88. 3 Vols.

Berge, Claude. Hypergraphs: Combinatorics of Finite Sets Amsterdam: North-Holland, 1989.

  • Berge, Claude. Graphs, New York, NY: Elsevier Science, 1985. Second Revised Edition.

Biggs, Norman L. Algebraic Graph Theory New York, NY: Cambridge University Press, 1974.

    • Biggs, Norman L.; Lloyd, E. Keith; and Wilson, Robin J. Graph Theory, 1736--1936 New York, NY: Oxford University Press, 1986.

Bollobas, Bela. Random Graphs New York, NY: Academic Press, 1985.

  • Bollobas, Bela. Graph Theory: An Introductory Course New York, NY: Springer-Verlag, 1979.
      • Bondy, J. Adrian and Murty, U.S.R. Graph Theory with Applications New York, NY: American Elsevier, 1976.

Buckley, Fred and Harary, Frank. Distance in Graphs Reading, MA: Addison-Wesley, 1990.

  • Capobianco, M. and Molluzzo, J. Examples and Counterexamples in Graph Theory Amsterdam: North-Holland, 1978.
      • Chartrand, Gary and Lesniak, Linda. Graphs Digraphs, Belmont, CA: Wadsworth, 1986. Second Edition.
  • Chartrand, Gary. Introductory Graph Theory Mineola, NY: Dover, 1985. (Former title: Graphs as Mathematical Models.)
  • Fulkerson, D.R., ed. Studies in Graph Theory Washington, DC: Mathematical Association of America, 1975.

Gibbons, Alan. Algorithmic Graph Theory New York, NY: Cambridge University Press, 1985.

    • Gould, Ronald. Graph Theory Redwood City, CA: Benjamin Cummings, 1988.

Gross, Jonathan L. and Tucker, Thomas W. Topological Graph Theory New York, NY: John Wiley, 1987.

Harary, Frank. Graph Theory Reading, MA: Addison-Wesley, 1969.

Hartsfield, Nora and Ringel, Gerhard. Pearls in Graph Theory: A Comprehensive Introduction New York, NY: Academic Press, 1990.

Konig, Denes. Theory of Finite and Infinite Graphs New York, NY: Birkhauser, 1990.

  • Lovasz, Laszlo and Plummer, M. Matching Theory Amsterdam: North-Holland, 1986.
  • Ore, Oystein. Graphs and Their Uses Washington, DC: Mathematical Association of America, 1963, 1990.
  • Palmer, Edgar M. Graphical Evolution: An Introduction to the Theory of Random Graphs New York, NY: John Wiley, 1985.
  • Saaty, Thomas L. and Kainen, Paul C. The Four-Color Problem: Assaults and Conquest New York, NY: McGraw-Hill, 1977.

Steinbach, Peter. Field Guide to Simple Graphs Albuquerque, NM: Design Lab, 1990.

Trudeau, Richard J. Dots and Lines Kent, OH: Kent State University Press, 1976.

Tutte, W.T. Graph Theory Reading, MA: Addison-Wesley, 1984.

White, Arthur T. Graphs, Groups and Surfaces New York, NY: Elsevier Science, 1984.

    • Wilson, Robin J. and Watkins, J. Graphs: An Introductory Approach New York, NY: John Wiley, 1990.


Coding Theory

Beker, Henry and Piper, Fred. Cipher Systems: The Protection of Communications New York, NY: John Wiley, 1982.

Blahut, Richard E. Theory and Practice of Error Control Codes Reading, MA: Addison-Wesley, 1983.

Blake, Ian F. and Mullin, Ronald C. An Introduction to Algebraic and Combinatorial Coding Theory New York, NY: Academic Press, 1976.

Brassard, Gilles. Modern Cryptology: A Tutorial New York, NY: Springer-Verlag, 1988.

Cameron, P.J. and van Lint, J.H. Graphs, Codes and Designs New York, NY: Cambridge University Press, 1980.

Goppa, V.D. Geometry and Codes Norwell, MA: Kluwer Academic, 1988.

    • Hamming, Richard W. Coding and Information Theory, Englewood Cliffs, NJ: Prentice Hall, 1986. Second Edition.
  • Hill, Raymond. A First Course in Coding Theory New York, NY: Clarendon Press, 1986.

Konheim, Alan G. Cryptography: A Primer New York, NY: John Wiley, 1981.

    • MacWilliams, F.J. and Sloane, N.J.A. The Theory of Error-Correcting Codes Amsterdam: North-Holland, 1977.
  • Peterson, W. Wesley and Weldon, E.J., Jr. Error-Correcting Codes, Cambridge, MA: MIT Press, 1961, 1972. Second Edition.
      • Pless, Vera. Introduction to the Theory of Error-Correcting Codes, New York, NY: John Wiley, 1982, 1989. Second Edition.

Sloane, N.J.A. A Short Course on Error Correcting Codes New York, NY: Springer-Verlag, 1975.

      • Thompson, Thomas M. From Error-Correcting Codes Through Sphere Packings to Simple Groups Washington, DC: Mathematical Association of America, 1983.
  • Welsh, Dominic. Codes and Cryptography New York, NY: Clarendon Press, 1988.


Discrete Mathematics: Special Topics

Beth, Thomas; Jungnickel, Dieter; and Lenz, Hanfried. Design Theory New York, NY: Cambridge University Press, 1986.

Davey, B.A. and Priestley, H.A. Introduction to Lattices and Order New York, NY: Cambridge University Press, 1990.

    • Goldberg, Samuel I. Introduction to Difference Equations Mineola, NY: Dover, 1986.

Gratzer, George. General Lattice Theory New York, NY: Academic Press, 1978.

  • Mickens, Ronald E. Difference Equations New York, NY: Van Nostrand Reinhold, 1987.
  • Welsh, D.J.A. Matroid Theory New York, NY: Academic Press, 1976.

White, Neil, ed. Theory of Matroids New York, NY: Cambridge University Press, 1986.

    • Wilf, Herbert S. Generating Functionology New York, NY: Academic Press, 1990.

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