A determinant of symmetric forms |
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Authors: | K.V Menon |
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Affiliation: | Department of Mathematics, University of Benin, Benin City, Nigeria |
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Abstract: | Let Δ(α + β) = |Hλ2?r+1| where Hr is the complete symmetric function in (α1 + β1), (α2 + β2), …, (αn + βn). It is proved that Δ(α + β) ? Δ(α) + Δ(β). This inequality is generalised for certain symmetric functions defined by Littlewood. Let . Then we prove that Ω(α + β) ? Ω(α) + Ω(β). Here λ1, λ2, λ3, …, λn is a partition such that λn > λn?1 > ··· > λ2 > λ1. |
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