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Covering by planks and avoiding zeros of polynomials
Alexey Glazyrin, Roman Karasev, Alexandr Polyanskii
We note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex…
Topological lower bounds on the sizes of simplicial complexes and simplicial sets
Sergey Avvakumov, Roman Karasev
We prove that if an -dimensional space satisfies certain topological conditions then any triangulation of as well as any its representation as a simplicial set with cont…
Systolic inequalities for the number of vertices
Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard +1
Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in…