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13.
Triangulations of Cayley and Tutte polytopes
Konvalinka, Matjaž ; Pak, Igor
Pred kratkim so bili definirani Cayleyjevi politopi kot konveksne ogrinjače Cayleyjevih kompozicij, ki jih je vpeljal Cayley leta 1857. V članku dokažemo Braunovo domnevo, ki izraža prostornino ...Cayleyjevega politopa s številom povezanih grafov. Rezultat razširimo na deformacijo z dvema spremenljivkama, ki ji rečemo Tuttov politop. Njegova prostornina se izraža s Tuttovim polinomom polnega grafa. Naš pristop temelji na eksplicitni triangulaciji Cayleyjevega in Tuttovega politopa. Dokažemo, da simpleksi v triangulaciji pripadajo označenim drevesom in gozdovom. Srce dokaza je direktna bijekcija, ki temelji na algoritmu "najprej sosedje" za pot po drevesu.
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