## The local $$h$$-polynomial of the edgewise subdivision of the simplex.(English)Zbl 1425.05163

Summary: The $$r$$-fold edgewise subdivision is a well studied flag triangulation of the simplex with interesting algebraic, combinatorial and geometric properties. An important enumerative invariant, namely the local $$h$$-polynomial, of this triangulation is computed and shown to be $$\gamma$$-nonnegative by providing explicit combinatorial interpretations to the corresponding coefficients. A construction of a flag triangulation of the seven-dimensional simplex whose local $$h$$-polynomial is not real-rooted is also described.

### MSC:

 05E45 Combinatorial aspects of simplicial complexes 52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) 55U10 Simplicial sets and complexes in algebraic topology
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### References:

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