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mathematical analysis > function > symmetric function > alternating polynomial

mathematical analysis > function > elementary function > polynomial > alternating polynomial

algebra > polynomial > alternating polynomial

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alternating polynomial

In algebra, an alternating polynomial is a polynomial ${\\displaystyle f(x_{1},\\dots ,x_{n})}$ such that if one switches any two of the variables, the polynomial changes sign:
${\\displaystyle f(x_{1},\\dots ,x_{j},\\dots ,x_{i},\\dots ,x_{n})=-f(x_{1},\\dots ,x_{i},\\dots ,x_{j},\\dots ,x_{n}).}$
Equivalently, if one permutes the variables, the polynomial changes in value by the sign of the permutation:
${\\displaystyle f\\left(x_{\\sigma (1)},\\dots ,x_{\\sigma (n)}\ ight)=\\mathrm {sgn} (\\sigma )f(x_{1},\\dots ,x_{n}).}$
More generally, a polynomial ${\\displaystyle f(x_{1},\\dots ,x_{n},y_{1},\\dots ,y_{t})}$ is said to be alternating in ${\\displaystyle x_{1},\\dots ,x_{n}}$ if it changes sign if one switches any two of the ${\\displaystyle x_{i}}$ , leaving the ${\\displaystyle y_{j}}$ fixed
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Alternating_polynomial)

polynôme alterné

francés

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http://data.loterre.fr/ark:/67375/PSR-BMFQ647R-D

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