On a constant arising in the asymtotic theory of symmetric groups
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 129-140
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Let $x_1(g)\ge x_1(g)\ge\dots$ be the lengths of the cycles of the permutation $g\in S_n$
and
$$
\widetilde\Sigma=\{(\sigma_1,\sigma_2,\dots):\,\sigma_1\ge\sigma_2\ge\dots,\ \sigma_1+\sigma_2+\dots=1\}
$$
The uniform probability distribution on $S_n$ and the map
$$
S_n\to\widetilde\Sigma:\,g\to(n^{-1}x_1(g),\,n^{-1}x_2(g),\dots)
$$
generate a probability distribution on $\widetilde\Sigma$. We investigate some properties of this distribution
when $n\to\infty$. In particular, we prove that the constant introduced in [1], [2] coincides with the Euler constant.
@article{TVP_1982_27_1_a11,
author = {Zv. Ignatov},
title = {On a constant arising in the asymtotic theory of symmetric groups},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {129--140},
publisher = {mathdoc},
volume = {27},
number = {1},
year = {1982},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a11/}
}
Zv. Ignatov. On a constant arising in the asymtotic theory of symmetric groups. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 129-140. http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a11/