Are there recommended books on computational geometry and polyhedral combinatoris?
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From: Casey Hawthorne on 21 Dec 2009 17:56 Are there recommended books on computational geometry and polyhedral combinatorics? In Volume 4 fascicles of TAoCP, Knuth says he is better at visualizing and manipulating algebraic formulas than objects in space, which relies on geometrical intuition. Are there other areas of combinatorics not covered by algebraic, geometric, and polyhedral combinatorics? -- Regards, Casey
From: tchow on 21 Dec 2009 21:07 In article <rsuvi5lnklkt7us2kthc4cd16vio6jg9je(a)4ax.com>, Casey Hawthorne <caseyhHAMMER_TIME(a)istar.ca> wrote: >Are there recommended books on computational geometry and polyhedral >combinatorics? There are subdisciplines here with very different flavors. For what I think you're looking for, I recommend that you check out any book with Janos Pach as a co-author. If you're more interested in combinatorial optimization, then you may want to look at books by Schrijver and/or Lovasz. If you're more interested in enumerative problems related to polytopes, and connections to algebraic geometry and topology, then you might check out the IAS/Park City volume on "Geometric Combinatorics" by Miller et al. >Are there other areas of combinatorics not covered by algebraic, >geometric, and polyhedral combinatorics? The first thing to come to mind is extremal combinatorics. This has quite a different flavor from the areas you mentioned. I mean things like Ramsey theory, Turan-type problems, etc. I still think of graph theory and design theory as being combinatorics, though they are practically their own separate disciplines nowadays. Combinatorics does not neatly partition into disjoint subsets. Enumerative combinatorics and probabilistic methods, for example, permeate all areas of combinatorics. If you have not read it already, I recommend Tim Gowers's article on "The Two Cultures of Mathematics." It explains how combinatorics is often characterized more by *methodology* than by *theory*. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
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