Erdos-Ko-Rado Theorem Paul Erdos 柯召 Richard Rado (1913-1996) (1910-2002) (1906-1989)
Erdős-Ko-Rado Theorem Paul Erdős (1913-1996) 柯召 (1910-2002) Richard Rado (1906-1989)
Erdos Rado Erdos 柯召
Erdős 柯召 Erdős Rado
Intersecting Families (》 intersecting: VS,T∈F,SnT≠0 trivial case:n<2k nontrivial examples: "How large can a nontrivial intersecting family be?
Intersecting Families F [n] k ⇥ ⇤S, T F, S ⌃ T ⇥= ⌅ intersecting: trivial case: n < 2k nontrivial examples: “How large can a nontrivial intersecting family be?
Erdos-Ko-Rado Theorem Let FC(),n≥2k. VSFTisEiferScotg proved in 1938; published in 1961; all S
Let F [n] k ⇥ , n ⇥ 2k. |F| ⇥ n 1 k 1 ⇥ Erdős-Ko-Rado Theorem ⇤S, TF is intersecting F, S ⌃ T ⇥= ⌅ proved in 1938; published in 1961; all S x x
Shifting Isoperimetric problem: With fixed perimeter, what plane figure has the largest area? Steiner symmetrization
With fixed perimeter, what plane figure has the largest area? Shifting Steiner symmetrization Isoperimetric problem: