Using Grassmann calculus in combinatorics: Lindström-Gessel-Viennot lemma and Schur functions
arXiv:1604.06276
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 Lindström-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.
10 pages, contribution to GASCom 2016; v2: minor corrections