On plane trees with a prescribed number of valency set realizationsстатья
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Аннотация:(перевод статьи http://mi.mathnet.ru/rus/fpm/v13/i6/p9)
We describe valency sets of plane bicolored trees with a prescribed number of realizations by plane trees. Three special types of plane trees are defined: chains, trees of diameter 4, and special trees of diameter 6. We prove that there is a finite number of valency sets that have R realizations as plane trees and do not belong to these special types. The number of edges of such trees is less than or equal to 12R + 2. The complete lists of valency sets of plane bicolored trees with 1, 2, or 3 realizations are presented.