Outside nested decompositions of skew diagrams and Schur function determinants

We describe the thickened strips and introduce the outside nested decompositions of any skew shape λ∕μ. For any such decomposition Φ=(Θ1,Θ2,…,Θg) of the skew shape λ∕μ where Θi is a thickened strip for every i, let r be the number of boxes that are contained in any two distinct thickened strips of Φ. Then we establish a determinantal formula of the function p1r(X)sλ∕μ(X) with the Schur functions of thickened strips as entries, where sλ∕μ(X) is the Schur function of the skew shape λ∕μ and p1r(X) is the power sum symmetric function indexed by the partition (1r). This generalizes Hamel and Goulden's theorem on the outside decompositions of the skew shape λ∕μ and our extension is motivated by the enumeration of m-strip tableaux, which was first counted by Baryshnikov and Romik via extending the transfer operator approach due to Elkies.