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A unifying approach for proving hook-length formulas for weighted tree families. (English) Zbl 1287.05009
There has been much recent activity on hook-length formulas for trees [G.-N. Han, Combinatorica 30, No. 2, 253–256 (2010; Zbl 1250.05017); W. Y. C. Chen et al., Electron. J. Comb. 16, No. 1, Research Paper R62, 16 p. (2009; Zbl 1180.05007); L. L. M. Yang, “Generalizations of Han’s hook length identities”, Preprint, arXiv:0805.0109]. This paper unifies and extends earlier results for hook-length formulas for trees by expanding the concept to weighted tree families.

MSC:
05A15 Exact enumeration problems, generating functions
05C05 Trees
05C22 Signed and weighted graphs
Software:
HookExp
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References:
[1] Aldous, D.: The continuum random tree. An overview. In: Stochastic Analysis, London Mathematical Society Lecture Notes Series, vol. 167, pp. 23-70, Cambridge University Press, Cambride (1991) · Zbl 0791.60008
[2] Bergeron F., Labelle G., Leroux P.: Combinatorial Species and Tree-Like Structures. Cambridge University Press, Cambridge (1998) · Zbl 0888.05001
[3] Chen W.Y.C., Gao O.X.Q., Guo P.L.: Hook length formulas for trees by Han’s expansion. Electron. J. Comb. 16,-#R62 (2009) · Zbl 1180.05007
[4] Flajolet P., Sedgewick R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009) · Zbl 1165.05001
[5] Gessel, I.; Sagan, B.; Yeh, Y.-N., Enumeration of trees by inversions, J. Graph Theory, 19, 435-459, (1995) · Zbl 0833.05045
[6] Gessel, I.; Seo, S., A refinement of cayley’s formula for trees, Electron. J. Comb., 11, #r27, (2006) · Zbl 1080.05005
[7] Gittenberger, B., Panholzer, A.: Some results for monotonically labelled simply generated trees. In: Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 173-180 (2005) · Zbl 1104.68084
[8] Han, G.-N., New hook length formulas for binary trees, Combinatorica, 30, 253-256, (2010) · Zbl 1274.05017
[9] Han, G.-N., Yet another generalization of postnikov’s hook length formula for binary trees, SIAM J. Discrete Math., 23, 661-664, (2009) · Zbl 1191.05004
[10] Han, G.-N., Discovering hook length formulas by an expansion technique, Electron. J. Comb., 15, #r133, (2008) · Zbl 1165.05305
[11] Kirschenhofer, P., On the average shape of monotonically labelled tree structures, Discrete Appl. Math., 7, 161-181, (1984) · Zbl 0528.05020
[12] Marckert, J.-F.; Miermont, G., Invariance principles of random bipartite planar maps, Ann. Probab., 35, 1642-1705, (2007) · Zbl 1208.05135
[13] Meir, A.; Moon, J.W., On the altitude of nodes in random trees, Can. J. Math., 30, 997-1015, (1978) · Zbl 0394.05015
[14] Panholzer, A.; Prodinger, H., Bijections for ternary trees and non-crossing trees, Discrete Math., 250, 181-195, (2002) · Zbl 1010.05018
[15] Postnikov, A., Permutohedra, associahedra, and beyond, Int. Math. Res. Notices, 6, 1026-1106, (2009) · Zbl 1162.52007
[16] Prodinger, H.; Urbanek, F.J., On monotone functions of tree structures, Discrete Appl. Math., 5, 223-239, (1983) · Zbl 0508.05042
[17] Sagan, B.E.: Probabilistic proofs of hook length formulas involving trees. Séminaire Lotharingien de Combinatoire, vol. 61A. Article B61Ab (2009) · Zbl 1230.05045
[18] Stanley R.: Enumerative Combinatorics, vol. 2. Cambridge University Press, Cambridge (1999) · Zbl 0928.05001
[19] Yang, L.L.M.: Generalizations of Han’s Hook length identities. arXiv:0805.0109
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