Séminaire Lotharingien de Combinatoire, B10q (1984), 2 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1987, 340/S-10, p. 92-93.]

David M. Jackson

Symmetric Functions and P-Recursiveness

Abstract. Let ck(n) be the number of k-regular simple labelled graphs on n vertices. The P-recursiveness of ck(n) for k = 2 has been shown by Anand Dumir and Gupta [Duke Math. J. 33 (1966) 757-770], for k = 3 by Read [J. London Math. Soc. 35 (1960) 344-351] for k = 4 by Read and Wormald [J. Graph Theory 4 (1980) 203-212], and for k = 5 by Goulden and Jackson [unpublished work - differential equation available upon request].

The purpose of this talk is to give a result about symmetric functions, which has application to the calculation of ck(n), and to raise the question of establishing the P-recursiveness of ck(n) for larger values of k [see also Goulden, Jackson and Reilly, SIAM J. Alg. Disc. Math. 4 (1983) 179-193].

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