✦ LIBER ✦
Two bijective proofs for the arborescent form of the Good–Lagrange formula and some applications to colored rooted trees and cacti
✍ Scribed by Michel Bousquet; Cedric Chauve; Gilbert Labelle; Pierre Leroux
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 598 KB
- Volume
- 307
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
✦ Synopsis
Goulden and Kulkarni (J. Combin. Theory Ser. A 80 (2) (1997) 295) give a bijective proof of an arborescent form of the Good-Lagrange multivariable inversion formula. This formula was ÿrst stated explicitly by Bender and Richmond (Electron. J. Combin. 5 (1) (1998) 4pp) but is implicit in . In this paper, we propose two new simple bijective proofs of this formula and we illustrate the interest of these proofs by applying them to the enumeration and random generation of colored rooted trees and rooted m-ary cacti.