Avoid notation if possible. Notation makes it really hard to search electronically.
Put the subject in context, e.g., "In a recent paper, T. Lehrer introduced the concept of left-bifurcled rectangles. He conjectured no such rectangles exist when the number of bifurcles $n$ is odd."
State your results, in non-technical language, if possible. "In this paper we show the existence of left-bifurcled rectangles for all prime $n$."
Mention a technique, if there is a new one: "Our methods involve analytic and algebraic topology of locally euclidean metrizations of infinitely differentiable Riemannian manifolds".
Never, ever, ever, cite papers in the bibliography by giving citation numbers; the abstract is an independent entity that should stand on its own.
Jeffrey Shallit
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