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Athanasiadis, Christos A.

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

Bull. Hell. Math. Soc. 60, 11-19 (2016).
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

Keywords:

simplicial complex; edgewise subdivision; local \(h\)-polynomial; Smirnov word; \(\gamma\) polynomial; real-rooted polynomial
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\textit{C. A. Athanasiadis}, Bull. Hell. Math. Soc. 60, 11--19 (2016; Zbl 1425.05163)
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