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Pattern-avoiding permutation classes
 Opler, Michal ; Jelínek, Vít (advisor) ; Klazar, Martin (referee)
For a permutation π, the major index of π is the sum of all indices i such that πi > πi+1. In this thesis, we study the distribution of the major index over pattern-avoiding permutations of length n. We focus on the number Mm n (Π) of permutations of length n with major index m and avoiding the set of patterns Π. First, we are able to show that for a singleton set Π = {σ} other than some trivial cases, the values Mm n (Π) are monotonic in the sense that Mm n (Π) ≤ Mm n+1(Π). Our main result is a study of the asymptotic behaviour of Mm n (Π) as n goes to infinity. We prove that for every fixed m, Π and n large enough, Mm n (Π) is equal to a polynomial in n and moreover, we are able to determine the degrees of these polynomials for many sets of patterns. 1
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