Abstract
A Theorem of Hou, Leung and Xiang generalised Kneser’s addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an alternative proof of the theorem that also holds in the non-separable case, thus solving Hou’s conjecture. This result is a consequence of a strengthening of Hou et al.’s theorem that is inspired by an addition theorem of Balandraud and is obtained by combinatorial methods transposed and adapted to the extension field setting.
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Financial support for this research was provided by the “Investments for the future" Programme IdEx Bordeaux CPU (ANR-10-IDEX-03-02) and the Spanish Ministerio de Economía y Competitividad under project MTM2014-54745-P.
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Bachoc, C., Serra, O. & Zémor, G. Revisiting Kneser’s Theorem for Field Extensions. Combinatorica 38, 759–777 (2018). https://doi.org/10.1007/s00493-016-3529-0
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DOI: https://doi.org/10.1007/s00493-016-3529-0