Six etudes in generating functions
- 1 January 1989
- journal article
- research article
- Published by Taylor & Francis in International Journal of Computer Mathematics
- Vol. 29 (2-4) , 201-215
- https://doi.org/10.1080/00207168908803760
Abstract
Schutzenberger's philosophy of getting algebraic generating functions out of context-free languages is practiced to obtain short proofs of results of Kreweras, Kreweras-Poupard and Kreweras-Moszkowski, concerning the refined enumeration of legal bracketings according to various parameters. We also mention some ramifications to the enumeration of ordered trees. As an “encore”, we give a short proof of a formula, conjectured by Kirkman and first proved by Cayley, that counts the number of ways of placing m non-intersecting diagonals in a convex polygon of k sides. 1980 Mathematics Subject Classification: 68R05, 68Q45, 05A15.Keywords
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