Separating modules of support-degree k equate to O(k)-subgraph counts, those of symmetric circuit size n^Θ(k) equate to Θ(k)-WL, and their multiplicities equate to differing automorphism cycle indices.
Intersecting Families of Permutations
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
A set of permutations $I \subset S_n$ is said to be {\em k-intersecting} if any two permutations in $I$ agree on at least $k$ points. We show that for any $k \in \mathbb{N}$, if $n$ is sufficiently large depending on $k$, then the largest $k$-intersecting subsets of $S_n$ are cosets of stabilizers of $k$ points, proving a conjecture of Deza and Frankl. We also prove a similar result concerning $k$-cross-intersecting subsets. Our proofs are based on eigenvalue techniques and the representation theory of the symmetric group.
representative citing papers
A new necessary condition is established that Y must be partition-transitive w.r.t. certain partitions of n for (T_n, Y) to tile S_n, generalizing Rothaus-Thompson and Nomura, with a conjecture that neither T_n nor T_n* tiles S_n for n >= 4.
citing papers explorer
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Graph Isomorphism and Representation Theory
Separating modules of support-degree k equate to O(k)-subgraph counts, those of symmetric circuit size n^Θ(k) equate to Θ(k)-WL, and their multiplicities equate to differing automorphism cycle indices.
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Tiling the symmetric group by transpositions
A new necessary condition is established that Y must be partition-transitive w.r.t. certain partitions of n for (T_n, Y) to tile S_n, generalizing Rothaus-Thompson and Nomura, with a conjecture that neither T_n nor T_n* tiles S_n for n >= 4.