Jie Wang

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20242026

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math.CO2025

A lower bound theorem for $d$ -polytopes with at most $3 d - 1$ vertices

Guillermo Pineda-Villavicencio, Jie Wang

We prove a lower bound theorem for the number of $k$ -faces ( $1 \leq k \leq d - 2$ ) in a $d$ -dimensional polytope $P$ (or $d$ -polytope) with up to $3 d - 1$ vertices. Previous lower bound th…

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, Grünbaum conjectured that the function $ϕ_{k} (d + s, d) := (k + 1 d + 1) + (k + 1 d) - (k + 1 d + 1 - s), for 2 \leq s \leq d$ provides the minimum number of $k$ -…

A lower bound theorem for d-polytopes with at most 3d−1 vertices

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

A lower bound theorem for $d$ -polytopes with at most $3 d - 1$ vertices

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