Sums of binomial determinants, non-intersecting lattice paths and positivity of Chern-Schwartz-MacPherson classes

Details Sums of binomial determinants, non-intersecting lattice paths and positivity of Chern-Schwartz-MacPherson classes Sums of binomial determinants, non-intersecting lattice paths and positivity of Chern-Schwartz-MacPherson classes

2007-02-19

arxiv.org/abs/math/0702566v1

Mathematics

Combinatorics

10 pages, 5 figures, comments are welcome

Scientific paper

We give a combinatorial interpretation of a certain positivity conjecture of Chern-Schwartz-MacPherson classes, as stated by P. Aluffi and the author in a previous paper. It translates into a positivity property for a sum of p by p determinants consisting of binomial coefficients, generalizing the classical Theorem of Lindstrom-Gessel-Viennot et al. which computes these determinants in terms of non-intersecting lattice paths. We prove this conjecture for p=2,3.

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