Geodesic
Nilpotent subsemigroups of a~semigroup of order-decreasing transformations of a~rooted tree
Algebra and discrete mathematics, no. 4 (2006), pp. 126-140.

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This paper deals with a semigroup of order-decreasing transformations of a rooted tree. Such are the transformations $\alpha$ of some rooted tree $G$ satisfying following condition: for any $x$ from $G$ $\alpha(x)$ belongs to a simple path from $x$ to the root vertex of $G$. We describe all subsemigroups of the mentioned semigroup, which are maximal among nilpotent subsemigroups of nilpotency class $k$ in our semigroup. In the event when rooted tree is a ray we prove that all these maximal subsemigroups are pairwise nonisomorphic.
Keywords: semigroup, order-decreasing, non-isomorphic. 
@article{ADM_2006_4_a8,
     author = {A. Stronska},
     title = {Nilpotent subsemigroups of a~semigroup of order-decreasing transformations of a~rooted tree},
     journal = {Algebra and discrete mathematics},
     pages = {126--140},
     publisher = {mathdoc},
     number = {4},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2006_4_a8/}
}
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A. Stronska. Nilpotent subsemigroups of a~semigroup of order-decreasing transformations of a~rooted tree. Algebra and discrete mathematics, no. 4 (2006), pp. 126-140. http://geodesic.mathdoc.fr/item/ADM_2006_4_a8/