Sometimes, it is useful to fix a choice of representative element from each equivalence class of a partition. For example, a preferred element in each coset. I know this has a name; but frustratingly I cannot remember it or find it on google.
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Thomas Andrews
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Mithrandir
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A choice function? – Christophe Boilley Feb 07 '25 at 15:26
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@ChristopheBoilley Although a reasonable name, I am confident there is a specific term used in combinatorics for equivalence classes specifically – Mithrandir Feb 07 '25 at 15:28
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A representative then? – Christophe Boilley Feb 07 '25 at 15:29
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2"System of representatives," I think? – Thomas Andrews Feb 07 '25 at 15:31
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3System of distinct representatives? – Robert Israel Feb 07 '25 at 15:31
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Googling "system of representatives," it looks like it is most commonly "system of distinct representatives." Ah, I see @RobertIsrael got there, too. – Thomas Andrews Feb 07 '25 at 15:33
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System of distinct representatives is what I'm looking for, thanks! If one of ya'll wants to post this as an answer I will accept it. – Mithrandir Feb 07 '25 at 15:35
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1See also https://en.wikipedia.org/wiki/Transversal_(combinatorics) – lhf Feb 07 '25 at 15:36
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To be fair, these are the kind of mathematical questions that any AI chatbot can answer for you. (Always be careful of course, but once you have the term, you can easily verify if it is correct or not.) – Martin Brandenburg Feb 08 '25 at 22:50
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"System of distinct representatives" is the usual term.
Thomas Andrews
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The usual term is "system of representatives". The "distinct" is already included in the meaning of "representative". Also, formally it is a set, so saying that the elements are distinct is funny anyway. Also, please don't answer questions which have +10 duplicate targets. (If a question mentions and defines this standard term here, it is a duplicate target. It doesn't have to be the exact same definition question. I have added some. There are many more.) – Martin Brandenburg Feb 08 '25 at 22:56
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That was my initial inclination, but I found a lot more usages with "distinct" than not. @MartinBrandenburg Also, they are distinct as representatives - there is only one per equivalence class. – Thomas Andrews Feb 08 '25 at 23:12