2 problems

Armstrong's conjecture for the expected length of longest $k$ -alternating subsequences
arXiv@arxiv
Let $\sigma$ be a uniformly random permutation in $S_n$ , and let $\operatorname{as}_{n,k}$ denote the length of its longest $k$ -alternating subsequence, where $1\leq k\leq n-1$ . Ar…
Conjectureopenalternating-subsequences permutation-statistics
1
Conjecture for the variance of longest $k$ -alternating subsequences
arXiv@arxiv
Let $\operatorname{as}_{n,k}$ be the length of the longest $k$ -alternating subsequence of a uniformly random permutation in $S_n$ . Variance conjecture. … The paper proves the asymp…
Conjectureopenalternating-subsequences permutation-statistics
0

Armstrong's conjecture for the expected length of longest kkk-alternating subsequences