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What are the eigenvectors of the graph Laplacian of a Johnson graph J(n,k)?
Since the Johnson graphs are regular, the Laplacian eigenvectors are the eigenvectors of the adjacency matrix. The Johnson graphs belong to an association scheme, the Johnson scheme, and explicit ...
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What are the eigenvectors of the graph Laplacian of a Johnson graph J(n,k)?
These questions are all answered in the Wikipedia article Johnson graph. As Chris noted, it doesn't matter if you consider the adjacency matrix or the Laplacian matrix. The eigenvectors stay the same ...
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3
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Accepted
Source for: a permutation group is multiplicity-free if and only if its 2-orbits define an association scheme
This is indeed known, and can be found, for instance, in the book "Algebraic combinatorics. I. Association schemes" by Bannai and Ito (1984), Section II.2, Example 2.1 (p. 53).
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Showing equality of Eberlein polynomials
Multiply each sum by $x^i y^n$. Sum on $n$, then $i$, then $r$. In both cases we get
$$y^{k+j}(1-y)^{j-k-1}(1-x)^j(1-y+xy)^{k-j}.$$
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What are the eigenvectors of the graph Laplacian of a Johnson graph J(n,k)?
With Chris' and Brendan's feedback, I found Delsarte's and Levenstein's paper on Association schemes and coding theory which explicitly gives the solution for this. The idempotents of the Johnson ...
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