Divisibility of binomial coefficients and generation of alternating groups

Abstract

We examine an elementary problem on prime divisibility of binomial coefficients. Our problem is motivated by several related questions on alternating groups.

16 pages, 1 figure; ancillary attachments include computer code and output. v2 has improved asymptotic density estimates and other minor fixes. v3 has minor fixes for publication

References in corpus (1)

• Invariable generation of the symmetric group

Cited by in corpus (3)

• Almost all alternating groups are invariably generated by two elements of prime order
• On invariable generation of alternating groups by elements of prime and prime power order
• Invariable generation of finite simple groups and rational homology of coset posets