Questions tagged [association-schemes]

Association schemes belong to both algebra and combinatorics. They provide a unified approach to many topics, for example combinatorial designs and block codes. Association schemes also generalize groups and character theory of linear representations of groups.

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Is this Cartan's Criterion for Semisimplicity

I am reading through a paper on semisimplicity of adjacency algebras of association schemes and the one example uses what seems to be the Cartan Criterion for a finite dimensional field of ...
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27 views

Characterization of Strongly Regular Graphs

I am looking for a reference in which I can find a proof of the following result. A strongly regular graph is disconnected if and only if it is a disjoint union of complete graphs $K_n$ of the same ...
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40 views

Cyclotomic scheme is a Association scheme

I try to show that the following defines an association scheme: Let $\mathbb{F}_q$ be a field, $\omega$ a primitive element of $\mathbb{F}_q^\times$ and $s$ divides $q-1$. Define $r=\frac{q-1}{s}$, $...
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110 views

Proof that the conjugacy class association scheme is an association scheme

I was looking at the conjugacy class association scheme (where, given some group $G$, each conjugacy class $C_i$ gets a relation $R_i$, where $R_i=\{(x,y)|xy^{-1}\in C_i\}$), and trying to show that ...
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references of discrete association scheme

I tried to find a book or paper to understanding discrete association scheme but I could not get any book for that. What is the good references for that?
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35 views

$\left(n+1\right)\times \left(n+1\right)$ algebra isomorphic to Bose-Mesner algebra?

The Wikipedia article on association schemes claims regarding Bose-Mesner algebras: There is another algebra of $\left(n+1\right)\times \left(n+1\right)$ matrices which is isomorphic to ${\mathcal {...
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162 views

Example of non-commutative association scheme

I need an example of non-commutative association scheme of ordered 6. I tried to use the example in the book Handbook of Combinatorial Designs, Second Edition by Charles J. Colbourn‏،Jeffrey H. Dini ...
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62 views

Which informations should I need to know about adjacency algebra or Bose-Mesner algebra?

Does anyone know about adjacency algebra or Bose-Mesner algebra? I have read about that, but I don't know what it says. I want to know the basic information I need to know the basis $<E_{i}>$....