Geodesic
Duality of graded graphs
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 4, pp. 357-404.

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Summary: A graph is said to be graded if its vertices are divided into levels numbered by integers, so that the endpoints of any edge lie on consecutive levels. Discrete modular lattices and rooted trees are among the typical examples. The following three types of problems are of interest to us: (1) path counting in graded graphs, and related combinatorial identities;
Keywords: enumerative combinatorics, tableaux, Young diagram, differential poset, graded graph 
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Fomin, Sergey. Duality of graded graphs. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 4, pp. 357-404. http://geodesic.mathdoc.fr/item/JAC_1994__3_4_a1/