A solution to the combinatorial puzzle of Mayer’s virial expansion
Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 3, pp. 229-262.

Mayer’s second theorem in the context of a classical gasmodel allows us to write the coe�fficients of the virial expansion of pressure in terms of weighted two-connected graphs. Labelle, Leroux and Ducharme studied the graph weights arising from the one-dimensional hardcore gas model and noticed that the sum of these weights over all two-connected graphs with n vertices is –n(n–2)!. Th�is paper addresses the question of achieving a purely combinatorial proof of this observation and extends the proof of Bernardi for the connected graph case.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/18
Classification : 82-XX, 05-XX
Mots-clés : Virial expansion, cluster expansion, two-connected graph, involution, Tonks gas, hard-core gas 
@article{AIHPD_2015__2_3_229_0,
     author = {Tate, Stephen James},
     title = {A solution to the combinatorial puzzle of {Mayer{\textquoteright}s} virial expansion},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {229--262},
     volume = {2},
     number = {3},
     year = {2015},
     doi = {10.4171/aihpd/18},
     mrnumber = {3416836},
     zbl = {1337.82005},
     language = {en},
     url = {https://numdam.org/articles/10.4171/aihpd/18/}
}
TY  - JOUR
AU  - Tate, Stephen James
TI  - A solution to the combinatorial puzzle of Mayer’s virial expansion
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2015
SP  - 229
EP  - 262
VL  - 2
IS  - 3
UR  - https://numdam.org/articles/10.4171/aihpd/18/
DO  - 10.4171/aihpd/18
LA  - en
ID  - AIHPD_2015__2_3_229_0
ER  - 
%0 Journal Article
%A Tate, Stephen James
%T A solution to the combinatorial puzzle of Mayer’s virial expansion
%J Annales de l’Institut Henri Poincaré D
%D 2015
%P 229-262
%V 2
%N 3
%U https://numdam.org/articles/10.4171/aihpd/18/
%R 10.4171/aihpd/18
%G en
%F AIHPD_2015__2_3_229_0
Tate, Stephen James. A solution to the combinatorial puzzle of Mayer’s virial expansion. Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 3, pp. 229-262. doi : 10.4171/aihpd/18. https://numdam.org/articles/10.4171/aihpd/18/
  • Procacci, Aldo Virial series for a system of classical particles interacting through a pair potential with negative minimum, Reviews in Mathematical Physics, Volume 34 (2022) no. 03 | DOI:10.1142/s0129055x22500064
  • Jansen, Sabine Revisiting Groeneveld’s approach to the virial expansion, Journal of Mathematical Physics, Volume 62 (2021) no. 2 | DOI:10.1063/5.0030148

Cité par 2 documents. Sources : Crossref