arXiv math/07025662007-02-19math.COmath.AG

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

Leonardo Constantin Mihalcea

备注：: 10 pages, 5 figures, comments are welcome

英文摘要：

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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