For a permutation $\pi=\pi_1\pi_2\cdots\pi_n$ written in one-line notation, an index $i$ for which $\pi_i > i$ is usually called an 'excedance.' To me, this seems like a mispelling of what should be 'exceedance': many dictionaries list 'exceedance' as a valid word, but none I can find consider 'excedance' a correct spelling of any word. Also, as far as I know, 'excedance' is pronounced like 'exceedance' (that is, ex-ceed-ance). But, while both 'excedance' and 'exceedance' are to some extent used for this permutation concept, it seems that 'excedance' is much more common.

Question: Does anyone know the origin of the spelling 'excedance' for this permutation concept? Is it an error which has become standard?

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    $\begingroup$ Sounds like a bad translation of either Latin or the French excédence. $\endgroup$ May 8, 2020 at 1:43
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    $\begingroup$ Although your reputation indicates you know the spirit of the site better than I do, it's hard for me to understand in what sense this is a question about research mathematics. $\endgroup$
    – LSpice
    May 8, 2020 at 2:32
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    $\begingroup$ I've seen questions here before about terminology, but if this is deemed inappropriate for the site I would understand that as well. $\endgroup$ May 8, 2020 at 2:40
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    $\begingroup$ en.wiktionary.org/wiki/excedance explicitly lists excedance as a misspelling of exceedance. $\endgroup$ May 8, 2020 at 8:52
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    $\begingroup$ @CarloBeenakker: interestingly that page has now been edited to list excedance as the correct spelling of the mathematical concept. $\endgroup$ Aug 27 at 22:15

1 Answer 1


Mea culpa. Comtet used the term excédence. When writing EC1 I needed an English term for this concept. For some reason I didn't like the word exceedance. I thought it looked better without the double e, analogous to proceed and procedure. Thus I made up the word excedance.

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    $\begingroup$ Couldn't imagine a more authoritative response. Thanks! $\endgroup$ May 8, 2020 at 14:15
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    $\begingroup$ It looks better to me too without the double e, but that might be because I've gotten used to it. $\endgroup$ May 8, 2020 at 16:00

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