Reversion of power series and the extended Raney coefficients
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- by Charles Ching-An Cheng, James H. McKay, Jacob Towber, Stuart Sui-Sheng Wang and David L. Wright PDF
- Trans. Amer. Math. Soc. 349 (1997), 1769-1782 Request permission
Abstract:
In direct as well as diagonal reversion of a system of power series, the reversion coefficients may be expressed as polynomials in the coefficients of the original power series. These polynomials have coefficients which are natural numbers (Raney coefficients). We provide a combinatorial interpretation for Raney coefficients. Specifically, each such coefficient counts a certain collection of ordered colored trees. We also provide a simple determinantal formula for Raney coefficients which involves multinomial coefficients.References
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Additional Information
- Charles Ching-An Cheng
- Affiliation: Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309-4401
- Email: cheng@vela.acs.oakland.edu
- James H. McKay
- Affiliation: Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309-4401
- Email: mckay@vela.acs.oakland.edu
- Jacob Towber
- Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614-3504
- Email: matjt@depaul.edu
- Stuart Sui-Sheng Wang
- Affiliation: Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309-4401
- Email: swang@vela.acs.oakland.edu
- David L. Wright
- Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130-4899
- Email: wright@einstein.wustl.edu
- Received by editor(s): April 4, 1994
- Additional Notes: The third author was supported in part by the National Science Foundation under Grant DMS-9012210. The fifth author was supported in part by the National Security Agency under Grant MDA-904-89-H-2049
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 1769-1782
- MSC (1991): Primary 13F25, 05A15, 05C05, 13P99; Secondary 32A05
- DOI: https://doi.org/10.1090/S0002-9947-97-01781-9
- MathSciNet review: 1390972