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. A specialisation of a transformation formula for multi-dimensional elliptic hyper-geometric series is used to provide compact, non-determinantal formulae for the generatingfunction with respect to the major index of standard Young tableaux of skew shapes of theform “staircase minus rectangle”. 1. Introduction. A standard Young tableau of skew shape λ/µ, where λ = (λ 1 ,λ 2 ,...,λ n ) and µ = (µ 1 ,µ 2 ,...,µ n ) are n-tuples of non-negative integers which are in non-increasing order and satisfy λ i ≥ µ i for all i, is an arrangement of the numbers 1,2,...,|Pλ−µ| (where the last quantity denotes the sum of the respective dierences of the integers, ni=1 (λ i − µ i )) of the formπ 1,µ 1 +1 π 1,λ 1 π 2,µ 2 +1 ... π 2,µ 1 +1 π 2,λ 2 ... ... ...π n,µ n +1 π n,λ n such that numbers along rows and columns are increasing. The majorindexof a standardYoung tableau T, denoted by maj(T), is dened as the sum over all i such that i+1 appearsin a lower row in T than i. It is well-known (see e.g. [19, Prop. 7.19.11 in combinationwith Theorem 7.16.1 and (7.10) with x

The major index generating function of standard Young tableaux of shapes of the form “staircase minus rectangle”