Some theorems @CihanPostsThms

Given a finite group G, write P(G) for the commuting probability of G, that is, the ratio of commuting ordered pairs in G x G. [Browning 2023]: Under the reverse ordering of rational numbers in [0,1], the set {P(G) : G finite} is well-ordered with order type ω^ω.

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Some theorems @CihanPostsThms

3 weeks ago

@selfattentive I don't know you. To me it is interesting that 42 being a sum of three perfect cubes was only a conjecture until 2019, when the numbers in the OP were found to work.

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Some theorems @CihanPostsThms

2 years ago

42 = (-80538738812075974)³ + (80435758145817515)³ + (12602123297335631)³

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Some theorems @CihanPostsThms

2 years ago

[Kirby–Siebenmann]. TOP/PL = K(ℤ/2, 3).

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Some theorems @CihanPostsThms

2 years ago

[Antonyan–Dobrowolski 2015]. For a locally compact Hausdorff group G with a closed subgroup H, TFAE: (1) G/H is locally contractible. (2) G/H is a manifold.

Some theorems @CihanPostsThms

3 years ago

[Antonyan 2011]: For a compact Hausdorff group G with a closed subgroup H, TFAE: (1) The coset space G/H is contractible. (2) H = G.

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Some theorems @CihanPostsThms

4 months ago

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Some theorems @CihanPostsThms

a month ago

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Some theorems @CihanPostsThms

2 years ago

[Bosboom–Demaine–Hesterberg–Lynch–Waingarten 2015]. It is PSPACE-hard to decide whether Player 1 has a forced win in a two-player Mario Kart race from given starting positions for the players.

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Some theorems @CihanPostsThms

8 months ago

Every position of Rubik's cube can be solved in at most 20 half-turn moves. Moreover there are positions for which 19 moves is not enough.

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Some theorems @CihanPostsThms

a month ago

It is conjectured that all zeros are simple.

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Some theorems @CihanPostsThms

a month ago

[Bui–Heath-Brown 2013]. If RH holds, then at least 19/27 of the zeros of the Riemann zeta-function are simple.

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Some theorems @CihanPostsThms

8 months ago

The upper bound is improved to 46 here: arxiv.org/abs/2409.15709

Some theorems @CihanPostsThms

4 years ago

43 ≤ R(5,5) ≤ 48 .

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Some theorems @CihanPostsThms

7 months ago

[Davis 1955]. Given a lattice (L, ≤), TFAE: (1) Every monotone f:L→L has a fixed point. (2) L is complete.

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Some theorems @CihanPostsThms

2 months ago

The product rule follows from the multivariate chain rule.

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Some theorems @CihanPostsThms

3 months ago

The unique pair consists of the right triangle with sides of lengths (377, 135, 352) and the isosceles triangle with sides of lengths (366, 366, 132).

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Some theorems @CihanPostsThms

3 months ago

A triangle is called rational if it has rational side lengths. [Hirakawa–Matsumura 2019]. Up to similitude, there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area.