Intersections of Sylow 2-subgroups in symmetric groups

Abstract We compute the asymptotic probability that a random pair of Sylow 2-subgroups in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>S</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> S_{n} or <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>A</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> A_{n} intersects trivially. This calculation complements recent work of Diaconis, Giannelli, Guralnick, Law, Navarro, Sambale, and Spink.