Using Grassmann calculus in combinatorics: Lindstr\"om-Gessel-Viennot   lemma and Schur functions
  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. 
Sylvain Carrozza, Thomas Krajewski, Adrian Tanasa
math.CO hep-th