David Yost

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math.CO2025

A lower bound theorem for $d$ -polytopes with $2 d + 2$ vertices

Guillermo Pineda-Villavicencio, Aholiab Tritama, Jie Wang +1

We establish a lower bound theorem for the number of $k$ -faces ( $1 \leq k \leq d - 2$ ) in a $d$ -dimensional polytope $P$ (abbreviated as a $d$ -polytope) with $2 d + 2$ vertices, extending t…

math.CO2025

A refined lower bound theorem for $d$ -polytopes with at most $2 d$ vertices

Guillermo Pineda-Villavicencio, Jie Wang, David Yost

In 1967, GrÃ¼nbaum conjectured that the function $I ¨ _{k} (d + s, d) := (k + 1 d + 1) + (k + 1 d) - (k + 1 d + 1 - s), for 2 \leq s \leq d$ provides the minimum number of $k…

math.CO2024

Polytopes with low excess degree

Guillermo Pineda-Villavicencio, Jie Wang, David Yost

We study the existence and structure of $d$ -polytopes for which the number $f_{1}$ of edges is small compared to the number $f_{0}$ of vertices. Our results are more elegantly expresse…

A lower bound theorem for d-polytopes with 2d+2 vertices

A refined lower bound theorem for d-polytopes with at most 2d vertices

Polytopes with low excess degree

A lower bound theorem for $d$ -polytopes with $2 d + 2$ vertices

A refined lower bound theorem for $d$ -polytopes with at most $2 d$ vertices