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Notes and References
THE COMBINATORICS OF THE ORDINARY
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adjacent alternating permutations altitude bijection branch decomposition called circular permutations coefficient combinatorial consider construction contains corresponding cycle Definition deleted differential equation distinct configurations distinguished substrings Durfee square element elementary counting lemmas elimination enumeration enumerative example exponential generating function Ferrers graph formal power series functional equation given gives identity integers labeled graphs labeled trees Lagrange theorem marking matrix maximal blocks maximal string decomposition maximal w,-strings monovalent vertices nonempty nonroot vertices number of edges number of partitions number of permutations number of sequences obtain occurrences ordered partition ordinary generating function outer face pattern plane partitions planted plane trees polynomial product lemma Proof Proposition recurrence equation required generating function required number respect result follows rises root edge root vertex rooted planar maps s-objects sequences of type Show step-set string decomposition theorem subsets tagged objects tion transformation lemma unique vertex weight function weighted path