Characterization of quasirandom permutations by a pattern sum. Issue 4 (27th August 2020) - Chan, Timothy F. N.
Abstract : It is known that a sequence { Π i } i ∈ N of permutations is quasirandom if and only if the pattern density of every 4‐point permutation in Π i converges to 1/24. We show that there is a set S of 4‐point permutations such that the sum of the pattern densities of the permutations from S in the permutations Π i converges to | S | / 24 if and only if the sequence is quasirandom. Moreover, we are able to completely characterize the sets S with this property. In particular, there are exactly ten such sets, the smallest of which has cardinality eight.