Additive decomposition schemes for polynomial functions over fields
Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2014), Additive decomposition schemes for polynomial functions over fields, Novi Sad Journal of Mathematics, 44, 2, p. 89-105
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01090554
Journal nameNovi Sad Journal of Mathematics
Novi Sad : Institut za matematiku
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Abstract (EN)The authors' previous results on the arity gap of functions of several variables are refined by considering polynomial functions over arbitrary fields. We explicitly describe the polynomial functions with arity gap at least 3, as well as the polynomial functions with arity gap equal to 2 for fields of characteristic 0 or 2. These descriptions are given in the form of decomposition schemes of polynomial functions. Similar descriptions are given for arbitrary finite fields. However, we show that these descriptions do not extend to infinite fields of odd characteristic.
Subjects / Keywordsfunction of several variables; arity gap; polynomial function; partial derivative
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