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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Composition of homomorphisms of association schemes
In Zieschang's "Theory of Association Schemes", in section 5.2, he remarks that the composition of homomorphisms is not always a homomorphism. I've been struggling to find an example of that ...
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Clique-coclique bound in association scheme
Let $A_0=I,A_1,\dots,A_k$ be the assocation matrices of a $k-$ class association scheme $R_0,\dots,R_k$ on a set $X$. Let $K \subset \{0,1,\dots,k\}$. We say a subset $Y \subset X$ is a $K-$coclique ...
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Understanding translation association schemes
I am having trouble understanding TAS.
Let $(X,+)$ be a finite abelian group. A translation assiociation scheme is an association scheme $(X, \mathbf{R})$so that for all $(x,y) \in R_i \implies (x+z,y+...
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Can we characterize the “associate classes” of a unipotent quasi-commutative quasigroup as some combinatorial design?
$I_n$ is the $n \times n$ or order $n$ identity matrix, $J_n$ is the order $n$ matrix of all ones, and $n \in \mathbb{Z}^+$.
We define a Latin square $\mathcal{L_n}$ to be a set of $n$ permutation ...
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Derivation of Kravchuk polynomial identity
I am working my way through N.J.A. Sloane "An Introduction to Association Schemes and Coding Theory" and have got stuck proving the last of his identities for the Kravchuck (Krawtchouk) ...
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In a primitive symmetric association scheme, why does $E_j$ occur in some power of $E_i$ for each $i,j$?
I am having some trouble in the proof of the Absolute Bound Condition for primitive symmetric association Schemes in the book Algebraic Combinatorics I by Bannai and Ito (Chapter 2, Section 4, Theorem ...
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Characterization of Strongly Regular Graphs [closed]
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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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 $r=\frac{q-1}{s}$, $...
user239922
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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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$\left(n+1\right)\times \left(n+1\right)$ 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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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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Does representation theory exists without Groups?
I need to know: is representation theory all about Groups?
Is it necessary to be a finite group?
Does representation theory exists without Groups?
For example is there sample where representation is ...
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