Multivariable Lagrange inversion, Gessel-Viennot cancellation, and the matrix tree theorem. (English) Zbl 0887.05005
A combinatorial proof of a new principal minor form of multivariable Lagrange inversion is given.
Reviewer: J.Cigler (Wien)
MSC:
| 05A15 | Exact enumeration problems, generating functions |
| 05C20 | Directed graphs (digraphs), tournaments |
| 05C38 | Paths and cycles |
| 05C05 | Trees |
References:
| [1] | R. B. Bapat, J. W. Grossman, D. M. Kulkarni, Generalized matchings and the all minors matrix tree theorem; R. B. Bapat, J. W. Grossman, D. M. Kulkarni, Generalized matchings and the all minors matrix tree theorem |
| [2] | Brooks, R. L.; Smith, C. A.B.; Stone, A. H.; Tutte, W. T., The dissection of rectangles into squares, Duke Math. J., 7, 312-340 (1940) · Zbl 0024.16501 |
| [3] | Chaiken, S., A combinatorial proof of the all minors matrix tree theorem, SIAM J. Algebraic Discrete Methods, 3, 319-329 (1982) · Zbl 0495.05018 |
| [4] | Ehrenborg, R.; Méndez, M., A bijective proof of infinite variated Good’s inversion, Advances in Math., 103, 221-259 (1994) · Zbl 0810.05070 |
| [5] | Gessel, I. M., A combinatorial proof of the multivariable Langrange inversion formula, J. Comb. Theory Ser. A, 45, 178-195 (1987) · Zbl 0651.05009 |
| [6] | I. M. Gessel, G. Viennot, Determinants, paths, and plane partitions; I. M. Gessel, G. Viennot, Determinants, paths, and plane partitions |
| [7] | Goulden, I. P.; Jackson, D. M., Combinatorial Enumeration (1983), Wiley-Interscience: Wiley-Interscience New York · Zbl 0519.05001 |
| [8] | Horn, R. A.; Johnson, C. R., Matrix Analysis (1985), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0576.15001 |
| [9] | Labelle, G., Une nouvelle démonstration combinatoire des formules d’inversion de Lagrange, Adv. Math., 42, 217-247 (1981) · Zbl 0477.05007 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
