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math.CO2016★ 31 cited
Pfaffians and nonintersecting paths in graphs with cycles: Grassmann algebra methods
Sylvain Carrozza, Adrian Tanasa
After recalling the definition of Grassmann algebra and elements of Grassmann--Berezin calculus, we use the expression of Pfaffians as Grassmann integrals to generalize a series of…
math.CO2016★ 29 cited
Using Grassmann calculus in combinatorics: Lindström-Gessel-Viennot lemma and Schur functions
Sylvain Carrozza, Thomas Krajewski, Adrian Tanasa
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…