Hamilton and Tait

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Lawson Tait, His Life and Work

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Michael Tait: Research Statement

My research uses algebraic and geometric methods to prove theorems in extremal combinatorics. Going the other way, I also use combinatorial methods to prove algebraic results. Algebraic methods are deeply embedded in my work and nearly all of my success in graph theoretic research has come from attacking purely combinatorial problems through the lens of algebra, combinatorial number theory, or ...

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The Tait Flyping Conjecture

We announce a proof of the Tait flyping conjecture; the confirmation of this conjecture renders almost trivial the problem of deciding whether two given alternating link diagrams represent equivalent links. The proof of the conjecture also shows that alternating links have no "hidden" symmetries. In the nineteenth century, the celebrated physicist and knot tabulator P. G. Tait proposed the foll...

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Tait in One Big Step

We present a Tait-style proof to show that a simple functional normaliser for a combinatory version of System T terminates. Using a technique pioneered by Bove and Capretta, we can implement the normaliser in total Type Theory. The main interest in our construction is methodological, it is an alternative to the usual small-step operational semantics on the one side and normalisation by evaluati...

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Variations on the Tait-Kneser theorem

At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...

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ژورنال

عنوان ژورنال: Nature

سال: 1911

ISSN: 0028-0836,1476-4687

DOI: 10.1038/087077a0