A Proof of Reutenauerʹs −q(n)Conjecture

C. Reutenauer (Adv. in Math.110(1995), 234–246) has defined a new class of symmetric functionsqλindexed by partitionsλ. He conjectures that forn⩾2, −q(n)is the sum of Schur symmetric functions. This paper provides a proof of his conjecture.