A closed form formula (generating function) for the Euler characteristic of the configuration space of n particles in a simplicial complex is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm89-1-4, author = {\'Swiatos\l aw R. Gal}, title = {Euler characteristic of the configuration space of a complex}, journal = {Colloquium Mathematicae}, volume = {89}, year = {2001}, pages = {61-67}, zbl = {0982.55012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm89-1-4} }
Światosław R. Gal. Euler characteristic of the configuration space of a complex. Colloquium Mathematicae, Tome 89 (2001) pp. 61-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm89-1-4/