mathlib documentation

combinatorics.choose.bounds

Inequalities for binomial coefficients #

This file proves exponential bounds on binomial coefficients. We might want to add here the bounds n^r/r^r ≤ n.choose r ≤ e^r n^r/r^r in the future.

Main declarations #

theorem choose_le_pow {α : Type u_1} [linear_ordered_field α] (r n : ) :
(n.choose r) n ^ r / r!
theorem pow_le_choose {α : Type u_1} [linear_ordered_field α] (r n : ) :
(n + 1 - r) ^ r / r! (n.choose r)