... 79 11 4, 19 94.[8] Merino, C.: Chip-firing and the Tutte polynomial. Annals of Combinatorics, 1, 253–259, 19 97.[9] Plautz J. and Calderer, R.: G-parking functions and the Tutte polynomial. Preprint. [10 ] ... Theorem 1 follows by the previousresult.A permutation σ ∈ Snis an up-down permutation if σ (1) < σ(2) > σ(3) < . . Let anbe the number of up-down permutation in Snfor n ≥ 1 and set ... present an algebraic proof of a resultwith the same flavour as the latter: Tn+2 (1, 1) = Tn(2, 1) , where Tn (1, 1) hasthe combinatorial interpretation of being the number of 0 1 2 increasing...