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- W2086284603 abstract "We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some results by Knuth and by Bousquet-Melou and Chapuy about embedded trees. We also give a new proof of the multivariate Lagrange inversion formula. Our strategy for counting trees is to exploit symmetries of refined enumeration formulas: proving these symmetries is easy, and once the symmetries are proved the formulas follow effortlessly. We also adapt this strategy to recover an enumeration formula of Goulden and Jackson for cacti counted according to their degree distribution." @default.
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- W2086284603 date "2014-04-01" @default.
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- W2086284603 title "Counting trees using symmetries" @default.
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- W2086284603 doi "https://doi.org/10.1016/j.jcta.2013.12.001" @default.
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