Abstract
In this paper we show that every n-additive symmetric function, between quite general structures like abelian groups and semigroups, can be factorized into a composition of additive function with the product of additive functions. We also show that every two n-additive functions, defined on a product of groups, with equal counterimages of the positive half-line must be proportional.
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Kucharski, R., Łukasik, R. The Form of Multi-additive Symmetric Functions. Results Math 73, 150 (2018). https://doi.org/10.1007/s00025-018-0911-9
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DOI: https://doi.org/10.1007/s00025-018-0911-9