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Mathoverflow.net news digest

  • 0 days

    Using the Schur complement determinant calculation procedure to prove the determ...

    Is it possible to use the Schur complement determinant calculation procedure to prove the determinant of transpose identity? The base case would be simple with dimensions n = 1, where det(a) = det(a_T). I am only a high school student, so I may not be...

  • 0 days

    Is this a proof of Stephan's Conjecture 19 (consecutive integers with odd contin...

    In his 2004 paper "Prove or Disprove: 100 Conjectures from the OEIS"(arXiv:math/0409509), Ralf Stephanconjectured (Conjecture 19):
    If $\mathrm{PCF}(n) = \mathrm{PCF}(n+1) \equiv 1 \pmod{2}$, then$n \equiv 1 \pmod{24}$.
    Here $\mathrm{PCF}(n)$ denotes the period length of the continued fractionexpansion of $\sqrt{n}$, for positive non-square $n$....

  • 15 years

    Most memorable titles

    Given the vast number of new papers / preprints that hit the internet everyday, one factor that may help papers stand out for a broader, though possibly more casual, audience is their title. This view was my motivation for asking this question almost...

  • 0 days

    Extension of a basic result in additive combinatorics

    Below is an apparently very basic result in additive combinatorics:
    Let $A,B \subseteq \mathbb{Z}$ be finite sets. Let $A+B = \{a+b : a \in A, b \in B\}$ be their sum-set. Then $|A+B| \geq |A| + |B| - 1$, with equality if and only if $A,B$ are arithmetic progressions with the same common difference....

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