Chromatic subdivision of simplicial complexes

Jan-Marten Brunink (Universität Osnabrück)

E1 05 (Leibniz-Saal)

Abstract

The chromatic subdivision $χ (Δ)$ of a simplicial complex $Δ$ is obtained by replacing the simplices of $Δ$ by suitable Schlegel diagrams of the cross-polytope.

We investigate the $f$ - and $h$ -vector transformation moving from $Δ$ to $χ (Δ)$ and its combinatorial interpretations in the same spirit as it was done for barycentric, edgewise and interval subdivisions.

Furthermore we study how algebraic invariants of the Stanley-Reisner ring as e.g, depth or projective dimension behave when passing from $Δ$ to its chromatic subdivision $χ (Δ)$ .

Graduate Student Meeting on Applied Algebra and Combinatorics Graduate Student Meeting on Applied Algebra and Combinatorics

MPI für Mathematik in den Naturwissenschaften Leipzig E1 05 (Leibniz-Saal)

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Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Tim Seynnaeve

Max Planck Institute for Mathematics in the Sciences, Leipzig

Rodica Dinu

University of Bucharest

Giulia Codenotti

Freie Universität Berlin

Frank Röttger

Otto-von-Guericke-Universität, Magdeburg