Combinatorial formulas for some generalized Ekeland-Hofer-Zehnder capacities of convex polytopes

Motivated by Pazit Haim-Kislev’s combinatorial formula for the Ekeland-Hofer-Zehnder capacities of convex polytopes, we give corresponding formulas for $$\Psi $$ -Ekeland-Hofer-Zehnder and coisotropic Ekeland-Hofer-Zehnder capacities of convex polytopes introduced by the second named author and others recently. Contrary to Pazit Haim-Kislev’s subadditivity result for the Ekeland-Hofer-Zehnder capacities of convex domains, we show that the coisotropic Hofer-Zehnder capacities satisfy the superadditivity for suitable hyperplane cuts of two-dimensional convex domains.