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Consider factorizations into transpositions of an n-cycle in the symmetric group S n. To every such factorization we assign a mono-mial in variables w ij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we… (More)

We introduce a new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length n and the set of parking functions of length n. For all u and v = 0, 1, 2, 3 and all n ≤ 7 we describe in terms of admissible pairs the dimensions of the bi-graded components h u,v of diagonal… (More)

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