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- W3143669468 abstract "In a recent breakthrough, Adiprasito, Avvakumov, and Karasev constructed a triangulation of the n-dimensional real projective space with a subexponential number of vertices. They reduced the problem to finding a small downward closed set-system (mathcal F) covering an n-element ground set which satisfies the following condition: For any two disjoint members (A, Bin mathcal F), there exist (ain A) and (bin B) such that either (Bcup {a}in mathcal F) and (Acup {b}{setminus }{a}in mathcal F), or (Acup {b}in mathcal F) and (Bcup {a}{setminus }{b}in mathcal F). Denoting by f(n) the smallest cardinality of such a family (mathcal F), they proved that (f(n)<2^{O(sqrt{n}log n)}), and they asked for a nontrivial lower bound. It turns out that the construction of Adiprasito et al. is not far from optimal; we show that (2^{(1.42+o(1))sqrt{n}}le f(n)le 2^{(1+o(1))sqrt{2nlog n}})." @default.
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- W3143669468 date "2021-01-01" @default.
- W3143669468 modified "2023-10-06" @default.
- W3143669468 title "Exchange Properties of Finite Set-Systems" @default.
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- W3143669468 doi "https://doi.org/10.1007/978-3-030-83823-2_99" @default.
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