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In 1995, Jockusch constructed an infinite family of centrally symmetric $3$-dimensional simplicial spheres that are cs-$2$-neighborly. Here we generalize his construction and show that for all $d\geq 3$ and $n\geq… Click to show full abstract
In 1995, Jockusch constructed an infinite family of centrally symmetric $3$-dimensional simplicial spheres that are cs-$2$-neighborly. Here we generalize his construction and show that for all $d\geq 3$ and $n\geq d+1$, there exists a centrally symmetric $d$-dimensional simplicial sphere with $2n$ vertices that is cs-$\lceil d/2\rceil$-neighborly. This result combined with work of Adin and Stanley completely resolves the upper bound problem for centrally symmetric simplicial spheres.
Keywords:
neighborly centrally;
highly neighborly;
symmetric spheres;
centrally symmetric
Journal Title: Advances in Mathematics
Year Published: 2020
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Journal Title: Advances in Mathematics
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!