A Vershik-Kerov theorem for wreath products

2024/08/08 by Chatterjee, Sourav, Diaconis, Persi · 1 citation
#05A05 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2408.04364

Abstract

Let G_n,k be the group of permutations of \1,2,…, kn\ that permutes the first k symbols arbitrarily, then the next k symbols and so on through the last k symbols. Finally the n blocks of size k are permuted in an arbitrary way. For σ chosen uniformly in G_n,k, let L_n,k be the length of the longest increasing subsequence in σ. For k,n growing, we determine that the limiting mean of L_n,k is asymptotic to 4√(nk). This is different from parallel variations of the Vershik-Kerov theorem for colored permutations.

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