2,795 research outputs found
Enumeration of Standard Young Tableaux
A survey paper, to appear as a chapter in a forthcoming Handbook on
Enumeration.Comment: 65 pages, small correction
Random Sorting Networks
A sorting network is a shortest path from 12...n to n...21 in the Cayley
graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform
random sorting network, as n->infinity the space-time process of swaps
converges to the product of semicircle law and Lebesgue measure. We conjecture
that the trajectories of individual particles converge to random sine curves,
while the permutation matrix at half-time converges to the projected surface
measure of the 2-sphere. We prove that, in the limit, the trajectories are
Holder-1/2 continuous, while the support of the permutation matrix lies within
a certain octagon. A key tool is a connection with random Young tableaux.Comment: 38 pages, 12 figure
Skew Howe duality and random rectangular Young tableaux
We consider the decomposition into irreducible components of the external
power regarded as a
-module. Skew Howe duality
implies that the Young diagrams from each pair which
contributes to this decomposition turn out to be conjugate to each other,
i.e.~. We show that the Young diagram which corresponds
to a randomly selected irreducible component has the same
distribution as the Young diagram which consists of the boxes with entries
of a random Young tableau of rectangular shape with rows and
columns. This observation allows treatment of the asymptotic version of this
decomposition in the limit as tend to infinity.Comment: 17 pages. Version 2: change of title, section on bijective proofs
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