2019/07/13 by Novik, Isabella, Zheng, Hailun
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1907.06115
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≥ 3 and n≥ 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.