The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
On the enumeration of skew Young tableaux
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Journal of Combinatorial Theory Series A
On Dimensions of a Random Solid Diagram
Combinatorics, Probability and Computing
q-Analog of tableau containment
Journal of Combinatorial Theory Series A
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Let T be a standard Young tableau of shape λ ⊢ k. We show that the probability that a randomly chosen Young tableau of n cells contains T as a subtableau is, in the limit n → ∞, equal to fλ/k!, where fλ is the number of all tableaux of shape λ. In other words, the probability that a large tableau contains T is equal to the number of tableaux whose shape is that of T, divided by k!. We give several applications, to the probabilities that a set of prescribed entries will appear in a set of prescribed cells of a tableau, and to the probabilities that subtableaux of given shapes will occur. Our argument rests on a notion of quasirandomness of families of permutations, and we give sufficient conditions for this to hold.