You're right, Anthony. The remnants of Gipson's Battalion Arkansas Mounted Rifles were attached to Cocke's/Polk's regiment.

This regiment, officially designated as the 39th Arkansas (but rarely, if ever, referred to as such in correspondence), started out as a "heavy" regiment -- Companies A through L -- but over time suffered losses and was reorganized as a standard 10-company regiment, to which Gibson's Battalion (Dis-) Mounted Rifles was attached, along with the dismounted remnants of an independent cavalry troop or two.