Geodesic
On extremal points of the space of symmetric stochastic matrices
Sbornik. Mathematics, Tome 25 (1975) no. 3, pp. 419-428 
V. N. Sachkov. On extremal points of the space of symmetric stochastic matrices. Sbornik. Mathematics, Tome 25 (1975) no. 3, pp. 419-428. http://geodesic.mathdoc.fr/item/SM_1975_25_3_a4/
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     title = {On extremal points of the space of symmetric stochastic matrices},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\Delta_n$ be the set of extremal points of the convex space of symmetric stochastic matrices of order $n$. Asymptotic formulas as $n\to\infty$ are found for the number of elements in $\Delta_n$, and limit distributions are given for the number of positive elements in a random probability matrix $C\in\Delta_n$ and for the characteristic multiplicity of a random mapping from a set of permutations in $\Delta_n$. Bibliography: 4 titles.

[1] G. Raizer, Kombinatornaya matematika, izd-vo «Mir», Moskva, 1966

[2] D. Riordan, Vvedenie v kombinatornyi analiz, IL, Moskva, 1963

[3] V. N. Sachkov, “Perechislitelnye zadachi kombinatornogo analiza”, Voprosy kibernetiki. Trudy seminara po kombinatornoi matematike, AN SSSR, Nauchnyi sovet po kompleksnoi probleme, «Kibernetika», 1973 | Zbl

[4] M. Katz, “On the extreme points of a certain convex polytore”, J. Comb. Theory, 8 (1970), 417–423 | DOI | MR | Zbl