Geodesic
Some Variants of the Exponential Formula, with Application to the Multivariate Tutte Polynomial (alias Potts Model)
Séminaire lotharingien de combinatoire, 61A (2009-2011) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

Voir la notice de l'acte

We prove some variants of the exponential formula and apply them to the multivariate Tutte polynomials (also known as Potts-model partition functions) of graphs. We also prove some further identities for the multivariate Tutte polynomial, which generalize an identity for counting connected graphs found by Riordan, Nijenhuis, Wilf and Kreweras and in more general form by Leroux and Gessel, and an identity for the inversion enumerator of trees found by Mallows, Riordan and Kreweras. Finally, we prove a generalization of Möbius inversion on the partition lattice. 

@article{SLC_2009-2011_61A_a4,
     author = {Alexander D. Scott and Alan D. Sokal},
     title = {Some {Variants} of the {Exponential} {Formula,} with {Application} to the {Multivariate} {Tutte} {Polynomial} (alias {Potts} {Model)}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2009-2011},
     volume = {61A},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a4/}
}
TY  - JOUR
AU  - Alexander D. Scott
AU  - Alan D. Sokal
TI  - Some Variants of the Exponential Formula, with Application to the Multivariate Tutte Polynomial (alias Potts Model)
JO  - Séminaire lotharingien de combinatoire
PY  - 2009-2011
VL  - 61A
UR  - http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a4/
ID  - SLC_2009-2011_61A_a4
ER  - 
%0 Journal Article
%A Alexander D. Scott
%A Alan D. Sokal
%T Some Variants of the Exponential Formula, with Application to the Multivariate Tutte Polynomial (alias Potts Model)
%J Séminaire lotharingien de combinatoire
%D 2009-2011
%V 61A
%U http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a4/
%F SLC_2009-2011_61A_a4
Alexander D. Scott; Alan D. Sokal. Some Variants of the Exponential Formula, with Application to the Multivariate Tutte Polynomial (alias Potts Model). Séminaire lotharingien de combinatoire, 61A (2009-2011). http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a4/