Geodesic
The action of the automorphism group of a finite graded partially ordered set on levels
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 63-72.

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The inequalities between the numbers of orbits of action of the automorphism group of a finite graded partially ordered set on the levels are obtained. The proofs are based on the notion of $\Delta$-reduced algebras of binary functions introduced in the paper. These algebras are analogies of the $\Delta$-reduced incidence algebras of finite partially ordered sets. 
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     author = {E. E. Marenich},
     title = {The action of the automorphism group of a finite graded partially ordered set on levels},
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     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a5/}
}
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E. E. Marenich. The action of the automorphism group of a finite graded partially ordered set on levels. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 63-72. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a5/