The Infinite Limit of Random Permutations Avoiding Patterns of Length Three [article]

Ross G. Pinsky
2018 arXiv   pre-print
For τ∈ S_3, let μ_n^τ denote the uniformly random probability measure on the set of τ-avoiding permutations in S_n. Let N^*=N∪{∞} with an appropriate metric and denote by S(N,N^*) the compact metric space consisting of functions σ={σ_i}_ i=1^∞ from N to N^* which are injections when restricted to σ^-1(N); that is, if σ_i=σ_j, i≠ j, then σ_i=∞. Extending permutations σ∈ S_n by defining σ_j=j, for j>n, we have S_n⊂ S(N,N^*). For each τ∈ S_3, we study the limiting behavior of the measures {μ_n^τ}_n=1^∞ on S(N,N^*).
arXiv:1806.07669v3 fatcat:w2jpl7gbsrgb5pemziaf6lyfuu