... the proof of Theorem 5.2. Therefore, Q is exactly the battery tableauobtained in the proof of Theorem 5.2, and so we have χλ, Γ(k,ν) = 1.Note that by Corollary 5.1, condition (a) of Theorem ... Rλ∪η. The next theorem follows from the results of [4, 6, 8, 10, 16, 23]. A summary of the relevant results in these papers and how they imply the following theorem is given in [23].Theorem ... > y, then the mth column of λ/(m) has anodd number of boxes. If m = y, then the xth column of λ/(m) has an odd number of boxes. In all cases, λ/(m) cannot be tiled by dominoes, and the result...