For n ≤ 27 we present exact values for the maximum number h(n) of halving lines and eh(n) of halving pseudolines, determined by n points in the plane. For this range of values of n we also present exact values of the rectilinear cr(n) and the pseudolinear e cr(n) crossing number of the complete graph Kn. eh(n) and e cr(n) are new for n ∈ {14, 16, 18, 20, 22, 23, 24, 25, 26, 27}, h(n) is new for...

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Let p $p$ be a fixed prime. We show that the number of isomorphism classes finite rings order n $p^n$ is α $p^\alpha$ , where = 4 27 3 + O ( 5 / 2 ) $\alpha =\frac{4}{27}n^3+\mathnormal {O}(n^{5/2})$ . This result was stated (with weaker error term) by Kruse and Price in 1969; problem with their proof pointed out Knopfmacher 1973. also commutative β $p^\beta$ $\beta =\frac{2}{27}n^3+\mathnormal...

Correct (for the execution) program might be untypable : let stupid n =. if n=n+1 then 27 else trué Etienne Miquey Realizing arithmetical formulae Classical realizability Realizability game Zoology Gender equality Introduction Curry-Howard Correct (for the execution) program might be untypable : let stupid n =. if n=n+1 then 27 else trué Etienne Miquey Realizing arithmetical formulae Classical ...