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.

8 questions
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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 ...
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 ...
40 views

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 $r=\frac{q-1}{s}$, $... 1answer 110 views Proof that the conjugacy class association scheme is an association scheme I was looking at the conjugacy class association scheme (where, given some group$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 ... 0answers 60 views 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? 1answer 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 {...
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 $<E_{i}>$....