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Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs. (English) Zbl 1243.14005
A sequence $$a_0, \dots, a_n$$ of real numbers is called log-concave if $$a_{i-1}a_{i+1}\leq a_i^2$$ for all $$i, 0<i<n$$.
The aim of the paper is to answer the following question.
Let $$\chi_G(t)=a_nt^n-a_{n-1}t^{n-1}+\cdots +(-1)^n a_0$$ be the chromatic polynomial of a graph $$G$$. Is the sequence $$a_0, \dots, a_n$$ log-concave? It is proved that for a matroid $$M$$ which is representable over a field of characteristic zero the coefficients of the characteristic polynomial of $$M$$ form a sign-alternating log-concave sequence of integers with no internal zeros.

##### MSC:
 14B05 Singularities in algebraic geometry 05B35 Combinatorial aspects of matroids and geometric lattices
CSM-A
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