  In theory of Coxeter groups, bigrassmannian elements are well known as
elements which have precisely one left descent and precisely one right descent.
In this article, we prove formulas on enumeration of bigrassmannian
permutations weakly below a permutation in Bruhat order in the symmetric
groups. For the proof, we use equivalent characterizations of bigrassmannian
permutations by Lascoux-Schutzenberger and Reading.
