# The Theory of Heaps and the Cartier-Foata Monoid

• Published in 2006
We present Viennot’s theory of heaps of pieces, show that heaps are equivalent to elements in the partially commutative monoid of Cartier and Foata, and illustrate the main results of the theory by reproducing its application to the enumeration of parallelogram polyominoes due to Bousquet–Mélou and Viennot.

### BibTeX entry

@misc{item56,
title = {The Theory of Heaps and the Cartier-Foata Monoid},
author = {C. Krattenthaler},
url = {http://www.mat.univie.ac.at/{\~{}}kratt/artikel/heaps.pdf},
urldate = {2015-12-03},
abstract = {We present Viennot’s theory of heaps of pieces, show that heaps are equivalent to elements in the partially commutative monoid of Cartier and Foata, and illustrate the main results of the theory by reproducing its application to the enumeration of parallelogram polyominoes due to Bousquet–M{\'{e}}lou and Viennot.},
comment = {},
collections = {},
year = 2006
}