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Eur J Comb
2011[Nov]; 32
(8
): 1282-1298
PMID27087722
show ga
We study unfair permutations, which are generated by letting [Formula: see text]
players draw numbers and assuming that player [Formula: see text] draws [Formula:
see text] times from the unit interval and records her largest value. This model
is natural in the context of partitions: the score of the [Formula: see text]th
player corresponds to the multiplicity of the summand [Formula: see text] in a
random partition, with the roles of minimum and maximum interchanged. We study
the distribution of several parameters, namely the position of player [Formula:
see text], the number of inversions, and the number of ascents. To perform some
of the heavy computations, we use the computer algebra package Sigma.