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The phrase "auction in which" is correct and usable in written English.
It can be used to describe a specific type of auction or to introduce a clause that provides more detail about the auction.
Example: "The auction in which rare artifacts were sold attracted many collectors from around the world."
Alternatives: "auction that" or "auction where".
Exact(60)
This was the first genuine auction in which the state was not short-changed.
It also ends a labored auction in which little interest in the company materialized.
Google sells ads using an online auction in which clients bid for certain search keywords.
This is what happens at a cattle auction or an art auction, in which people are shouting out bids.
The fully optimal mechanism is a non-standard auction in which bidders' payoffs are non-monotone in their opponents' bids.
In a competitive auction in which neither side was sure who could make what, West was doubled in five spades.
Another option is to hold an "English" (ascending-bid) auction in which institutional shareholders' bids can be observed.
Often goods are sold as part of an auction in which losing bidders have to forfeit their bids.
Boies said he could still see the bankruptcy court authorizing an auction in which Fox can match the highest bid.
The play was preceded by an auction, in which the opening bid for each pair was $12,500.
A start-up called Ibidcondo.com charges $100 for a seat at an auction in which a condo is sold.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com