Comments on: Coherent configurations and all that, 1 http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/ always busy counting, doubting every figured guess . . . Fri, 24 May 2013 07:17:33 +0000 hourly 1 http://wordpress.com/ By: Peter Cameron http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-9452 Mon, 17 Dec 2012 19:35:12 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-9452 Sorry, I don’t understand why, trying to do graph isomorphism, you throw away some cheap information.

]]> By: Durga http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-9439 Mon, 17 Dec 2012 14:58:51 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-9439 So, if our interest is only graph isomorphism problem then is it better not to necessiate clousre under transpose to get finer partition? Would the still result in cellular algebra, primarly the unique (0-1) basis of the algebra?

]]> By: Peter Cameron http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-9429 Mon, 17 Dec 2012 12:00:08 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-9429 If you didn’t have closure under transpose, then you could refine your relations still further, by intersecting them with their transposes, since a potential isomorphism preserving a bunch of relations also preserves their transposes.

]]> By: Durga http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-9420 Mon, 17 Dec 2012 04:13:17 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-9420 If I see coherent algebra as a tool to attack graph isomorphism problem as did by Weisfeilear without invoking group theory, I want to understand what is the meaning of clousure under transpose. I think i have intuitive understand of other conditions based on complet colouring of graph, sum being J means theat set of relation is partitioin, some subset adding to I means that diagonal elements are coloured differently than non-diogonal elments, closure under matrix multiplication has to do with partition being equitable. So what is the similar understanding of requiring closuer under transpose?

]]> By: Peter Cameron http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-6944 Tue, 18 Sep 2012 14:44:18 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-6944 That is a very good question. The definition works over the integers, as you say. But the most powerful results come from looking at the representation theory of the algebra, and even the difference between the complex and real numbers makes a big difference. In fact, statisticians (to whom all data is real) only work over the reals. I will come back to this point sometime, and try to say a bit more.

]]> By: Bjarki Holm http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-6943 Tue, 18 Sep 2012 12:05:09 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-6943 Dear Peter,

Thanks for a very nice summary of the development of coherent configurations.

Reading this, I have one question: when you define the algebra associatied with a coherent configuration, you consider the linear span of the basis matrices Ai over the complex numbers. Do you know if there is any particular reason to study these algebras over the complex numbers? This seems a bit strong as we really only need integral linear combinations of the basis matrices, via the numbers c_{ij}^k.

]]> By: Peter Cameron http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-4460 Sun, 01 Apr 2012 09:47:01 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-4460 Misha Klin has sent me a lot of information about the topic of this post. I will digest it and say something (including links) later in this series.

]]> By: Brain Boost* « Log24 http://cameroncounts.wordpress.com/2012/03/30/coherent-configurations-and-all-that-1/#comment-4447 Fri, 30 Mar 2012 16:02:30 +0000 http://cameroncounts.wordpress.com/?p=2199#comment-4447 [...] "Dark Fields" in this journal and Peter J. Cameron's weblog [...]

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