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Using Grassmann calculus in combinatorics: Lindström-Gessel-Viennot lemma and Schur functions (1604.06276v2)
Published 21 Apr 2016 in math.CO and hep-th
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.