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Short witnesses for Parikh-friendly permutations

2020
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The Australasian Journal of Combinatorics
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showed that for every permutation π of the ordered alphabet A = {a 1 , a 2 , . . . , a n } there exists a word w ∈ A * , in which each letter of A appears at least once, such that w and π(w) have the same Parikh matrix. He conjectured that it is always possible to find such a w whose length is at most 2n. We prove this. We use the usual notation for combinatorics on words. A word of m elements is x = x[1 . . m], with x[i] being the ith element and x[i . . j] the factor of elements from position

dblp:journals/ajc/Simpson20
fatcat:pyzczwf4mjdyvnd7xvpwkkewf4