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Quantized dual graded graphs. (English) Zbl 1230.05163
Summary: We study quantized dual graded graphs, which are graphs equipped with linear operators satisfying the relation $$DU - qU D = rI$$. We construct examples based upon: the Fibonacci differential poset, permutations, standard Young tableau, and plane binary trees.

##### MSC:
 05C30 Enumeration in graph theory 06A06 Partial orders, general 05C05 Trees 05C10 Planar graphs; geometric and topological aspects of graph theory
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