read HISTABRUT:
print(`Consider the random variable, studied by Richard Stanely: `):
print(` the largest up-down subsequence in a random n-permutation.`):
gu:=Yofseq(RS50(t),t,16,n,45,1,r):
print(`The mean is:`, gu[1]):
print(`The variance is:` , gu[2]):
print(`The asympotics to order 1, of the even alpha coefficients (the (2r)-th moment about the mean divided by the r-th power of the variance) `):
print(`as an expression in n and r is:`):
print(gu[3]):
print(`the (normalized) odd moments, to order 1, are`):
print(gu[4]):
print(``):
print(`In particular it is asymptotically normal (as proved by Stanely), but we have an even finer asympotics for the alpha coefficients. `):
print(`This took `, time(), `seconds . `):
quit: