Bijections for Cayley trees, spanning trees, and their q-analogues
نویسندگان
چکیده
منابع مشابه
Bijections for Cayley trees, spanning trees, and their q-analogues
We construct a family of extremely simple bijections that yield Cayley’s famous formula for counting trees. The weight preserving properties of these bijections furnish a number of multivariate generating functions for weighted Cayley trees. Essentially the same idea is used to derive bijective proofs and q-analogues for the number of spanning trees of other graphs, including the complete bipar...
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For a directed graph G on vertices {0, 1, . . . , n}, a G-parking function is an n-tuple (b1, . . . , bn) of non-negative integers such that, for every non-empty subset U ⊆ {1, . . . , n}, there exists a vertex j ∈ U for which there are more than bj edges going from j to G − U . We construct two bijective maps between the set PG of Gparking functions and the set TG of spanning trees of G rooted...
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According to the Fibonacci number which is studied by Prodinger et al., we introduce the 2-plane tree which is a planted plane tree with each of its vertices colored with one of two colors and qqppppppppppppppppp -free. The similarity of the enumeration between 2-plane trees and ternary trees leads us to build several bijections. Especially, we found a bijection between the set of 2-plane trees...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90004-x