Using Grassmann calculus in combinatorics: Lindstr\"om-Gessel-Viennot lemma and Schur functions
Combinatorics
2016-07-20 v2 High Energy Physics - Theory
Abstract
Grassmann (or anti-commuting) variables are extensively used in theoretical physics. In this paper we use Grassmann variable calculus to give new proofs of celebrated combinatorial identities such as the Lindstr\"om-Gessel-Viennot formula for graphs with cycles and the Jacobi-Trudi identity. Moreover, we define a one parameter extension of Schur polynomials that obey a natural convolution identity.
Cite
@article{arxiv.1604.06276,
title = {Using Grassmann calculus in combinatorics: Lindstr\"om-Gessel-Viennot lemma and Schur functions},
author = {Sylvain Carrozza and Thomas Krajewski and Adrian Tanasa},
journal= {arXiv preprint arXiv:1604.06276},
year = {2016}
}
Comments
10 pages, contribution to GASCom 2016; v2: minor corrections