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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A noncommutative generalization and $ q$-analog of the Lagrange inversion formula


Author: Ira Gessel
Journal: Trans. Amer. Math. Soc. 257 (1980), 455-482
MSC: Primary 05A15; Secondary 10A45
MathSciNet review: 552269
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Abstract: The Lagrange inversion formula is generalized to formal power series in noncommutative variables. A q-analog is obtained by applying a linear operator to the noncommutative formula before substituting commuting variables.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0552269-2
PII: S 0002-9947(1980)0552269-2
Keywords: Lagrange inversion, q-analog, factorization in free monoids, lattice path, q-Catalan numbers, continued fractions, labeled trees
Article copyright: © Copyright 1980 American Mathematical Society