The co-Pieri rule for Kronecker coefficients

A fundamental problem in the representation theory of the symmetric group, Sn, is to describe the coefficients in the decomposition of a tensor product of two simple representations. These coefficients are known in the literature as the Kronecker coefficients. The Littlewood–Richardson coefficients appear as an important subfamily of the wider class of stable Kronecker coefficients. This subfamily of coefficients can be calculated using a tableaux counting algorithm known as the Littlewood–Richardson rule. This paper generalises one half of this rule (the “co-Pieri” rule) to the the wider family of stable Kronecker coefficients.