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Results tagged with permutations
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user 934
Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.
12
votes
1
answer
256
views
GOE Version of Longest Increasing Subsequence
Let $S_n$ be the symmetric group equipped with uniform measure. For any $\pi\in S_n$, let $L_n=L_n(\pi)$ denote the longest increasing subsequence. A celebrated result of Baik, Deift and Johansson sta …
- 4,952
5
votes
1
answer
2k
views
Number of Permutations with k-inversions and with a single clamped value
Now, call the number of permutations with $k$-inversions $I_n(k)$. … Let $I^{\sigma(y)=x}_n(k)$ count the number of permutations $\sigma$ of length $n$ such that for a given (fixed) $x,y$ we have $\sigma(y)=x$. In other words I am forcing $y$ to be in bin $x$. …
- 4,952
4
votes
0
answers
97
views
Name for class of flattening permutations
Does this class of permutations have a common name? Have they been studied before? I've checked the lists at oeis.org (by cardinality) and findstat.org but didn't see anything. …
- 4,952
3
votes
0
answers
153
views
Exact growth rate of Longest Increasing Subsequence expectation
Let $S_n$ be the symmetric group, $\pi\in S_n$ a uniformly random permutation and $L_n:=L_n(\pi)$ denoting the length of the longest increasing subsequence (LIS). We know that $\lim_{n\rightarrow\inft …
- 4,952