Count basie pared down the role of piano in the rhythm section and pioneered the spontaneous, off-the-beat style of playing known as:

The answer is comping.

Comping is a musical term used in jazz and it comes from the word "accompanying". By comping guitarists, organists and pianists support and accompany the soloist. By doing that, they create a "glue" that holds the rhythm together. This technique was introduced by Count Basie and Duke Ellington.