TY - JOUR
T1 - A note on “Largest independent sets of certain regular subgraphs of the derangement graph”
AU - Filmus, Yuval
AU - Lindzey, Nathan
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024
Y1 - 2024
N2 - Let Dn,k be the set of all permutations of the symmetric group Sn that have no cycles of length i for all 1≤i≤k. In the paper mentioned above, Ku, Lau, and Wong prove that the set of all the largest independent sets of the Cayley graph Cay(Sn,Dn,k) is equal to the set of all the largest independent sets in the derangement graph Cay(Sn,Dn,1), provided n is sufficiently large in terms of k. We give a simpler proof that holds for all n, k and also applies to the alternating group.
AB - Let Dn,k be the set of all permutations of the symmetric group Sn that have no cycles of length i for all 1≤i≤k. In the paper mentioned above, Ku, Lau, and Wong prove that the set of all the largest independent sets of the Cayley graph Cay(Sn,Dn,k) is equal to the set of all the largest independent sets in the derangement graph Cay(Sn,Dn,1), provided n is sufficiently large in terms of k. We give a simpler proof that holds for all n, k and also applies to the alternating group.
KW - Alternating group
KW - Cayley graphs
KW - Derangements
KW - Erdos–Ko–Rado combinatorics
KW - Representation theory
KW - Symmetric group
UR - http://www.scopus.com/inward/record.url?scp=85187309541&partnerID=8YFLogxK
U2 - 10.1007/s10801-024-01304-3
DO - 10.1007/s10801-024-01304-3
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AN - SCOPUS:85187309541
SN - 0925-9899
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
ER -