# French word for “discrepancy” (mathematical term)?

What is the French term for "discrepancy" (the function that we use to evaluate the ability of a set-system to have the most balanced possible colouring (2 colours)) ? This article explains precisely what is discrepancy in graph theory/combinatorics.

(The purpose of this question is because I am doing a bachelor project in English about it but I am French so I would like to write about it in French on my resume but I can't find the exact term)

If you look in Wikipedia for "equidistributed sequence", the article defines "discrepancy". And this is indeed the definition you are looking for.

The French version of the article, suite équidistribuée, uses the word écart with the exact same formula.

The advantage of using discrépance (as suggested by XouDo) is that it's (I assume) borrowed from English, so people who know the term in English will immediately understand it. And indeed it has been used in this context; in fact, the French term discrépance isotrope has been translated (possibly mistranslated) back into English as isotrope discrepancy and is now a technical mathematical term (even though, grammatically, it should be probably be isotropic discrepancy).

The advantage of using écart is that it's a much more common word in French, so somebody who doesn't know the term in English might find it easier to grasp its meaning.

• Using the french word, plus mentioning the english term in parenthesis could be a good way to avoid ambiguity, especially when the french term is has a broad meaning like écrart. – XouDo Apr 5 at 13:58

It seems the word

discrépance

does exist as a mathematical term (never heard it before, personally), as you can see in Wikipedia : Suite à discrépance faible (English : Low-discrepancy sequence)

En mathématiques, une suite à discrépance faible est une suite ayant la propriété que pour tout entier N, la sous-suite x1, ..., xN a une discrépance basse.

I am not sure this is the exact same notion as the one you are looking for, though.

• Yes, I have seen it exists but when I look on the internet I don't find many things. – SAJ Apr 2 at 14:05

En complément, dans un lien produit dans une autre réponse, on trouve un lien vers une thèse en français :

La discrépance est une mesure de la non-uniformité d’une séquence de points distribués dans un cube unité multidimensionnel.

[ Eric Thiémard, Sur le calcul et la majoration de la discrépance à l'origine (Thèse de doctorat), École polytechnique fédérale de Lausanne, 2000 ]

Voilà qui est plus clair qu'une chose qui ne tend pas à l'equidistribution et qui fait que (mesure de) non-uniformité peut s'avérer utile selon le contexte.

Sans que ce soit relié spécifiquement, des termes similaires à écart, provenant du domaine de la statistique, sont peut-être aussi utiles pour expliquer couramment s'ils ne sont pas déjà associés à d'autres réalités : manque de concordance, désaccord, opposition, [écart], antinomie, contradiction (GDT).

As always, more details will be useful here. I believe that the French term you are looking for is discordance.

Doesn’t hysteresis convey that notion ? I’m not a specialist of your field. If it is correct, you should use that word, because it’s more widely spread amongst the scientific community, and it sounds less like an anglicism than « discrépance »