most recent 30 from http://mathoverflow.net 2013-05-25T08:12:08Z http://mathoverflow.net/feeds/question/85124 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85124/homotopical-combinatorics Shahrooz 2012-01-07T11:08:50Z 2012-01-13T22:19:22Z

<p>I have a question about the situation of homotopical combinatorics. There are many topics about combinatorial homotopy. But, I can't find any topic about homotopical combinatorics. More precisely, are there any definitions for some combinatorial objects as like as Latin Squares, Designs and etc in homotopy theory?</p> <p>Do we have any examples about the applications of homotopy theory in combinatorics and graph theory? I think there are some generalizations for the definitions of some combinatorial objects in the language of homotopy theory. </p> <p>Is this true thinking or not? Please guide me, if you have some experiences. </p>

http://mathoverflow.net/questions/85124/homotopical-combinatorics/85131#85131 Liviu Nicolaescu 2012-01-07T15:32:51Z 2012-01-07T15:32:51Z

<p><a href="http://www.informatik.uni-bremen.de/~dfk/" rel="nofollow">Dmitry Kozlov</a> has a book called <strong><em>Combinatorial Algebraic Topology</em></strong> where he does quite a bit of combinatorial homotopy. I suggest you have a look at this book. Maybe it will point you in the right direction.</p>

http://mathoverflow.net/questions/85124/homotopical-combinatorics/85616#85616 Ronnie Brown 2012-01-13T22:19:22Z 2012-01-13T22:19:22Z

<p>You might look at the papers of Rade T. Zivaljevic, particularly </p> <p>Živaljević, Rade T. Combinatorial groupoids, cubical complexes, and the Lovász conjecture. Discrete Comput. Geom. 41 (2009), no. 1, 135–161. </p> <p>and the references there, including a number of homotopical ones. There is an arXiv version of this paper. </p>