Some theorems
@CihanPostsThms
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Posting some theorems, and occasionally other stuff. By @bahran_cihan
Joined July 2022
NON-THEOREM ANNOUNCEMENT: As someone struggling with depression/isolation, one reason I opened this account is to get some sense of belonging with the math community. I would appreciate if you can refrain from "that is obvious duh", "you miss the point" type of comments. Thanks.
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RT @trajan317: Tonight I found out that the NSF math postdoctoral fellowship I applied for is being deleted because it does not comply with…
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RT @CihanPostsThms: An embedding of a graph in a book consists of • a linear order of its vertices along the spine of the book, and • an a…
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A positive integer is called *idoneal* if it cannot be written as ab+bc+ca for some integers 0<a<b<c. Theorem. The number of idoneal integers is either 65,66, or 67.
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RT @CihanPostsThms: Every closed finite-dimensional manifold, outside perhaps non-smoothable 4-manifolds*, has a (finite) CW-decomposition…
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RT @CihanPostsThms: [Ash 1975] (over ZF): If ℝ and ℂ are isomorphic as abelian groups, then ℝ has a subset which is not Lebesgue measurable.
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RT @CihanPostsThms: There exists a topology on ℚ which makes it a topological ring together with usual addition and multiplication, but the…
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RT @CihanPostsThms: [Guralnick–Kantor–Kassabov–Lubotzky 2011]. Every finite symmetric and alternating group has a presentation with 2 gener…
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RT @CihanPostsThms: [Morley 1899]: In any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral t…
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RT @CihanPostsThms: A Diophantine characterization of the factorial that goes through the alphabet:
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RT @CihanPostsThms: [Rademacher 1937]: The function p(n) := the number of partitions of n satisfies the following formula:
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@ahron_maline @corentinus37 1. No 2. Yes seem to be the answers at this stage from my limited googling exposure to the state of the art.
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@ahron_maline @corentinus37 I think the impossibility even for the whole set of positive integers was open before this. And whether k-coloring for without monochromatic Pythagorean triples for k>2 is possible still seems open.
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[Hambleton–Kreck 1988]. Given an integer e and a finite group G, the set of homeomorphism types of closed oriented 4-manifolds M with χ(M) = e, π₁(M) ≅ G is finite.
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