Séminaire Lotharingien de Combinatoire, B16e (1988), 10 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1987/S-16, p. 63-72.]
Daniel I. A. Cohen and Victor S. Miller
Obtaining Generating Functions from Ordered-Partition Recurrence Formulas
Abstract.
In solving two enumeration problems in chrmoatic graph theory it was discovered
that the natural recurrence formulas which developed included summing over
ordered-partitions. Using an infinite sum these formulas can be turned into generating
functions that lead to closed form expressions. This technique is illustrated
on the problem of counting how many ways a set of some non-intersecting
diagonals can be placed in an n-gon and on the problem of counting
non-crossing colorings of a cycle. These sequences are reminiscent of some work
of Carlitz and Riordan.
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