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The sentence 'collaboration between the three' is correct and can be used in written English.
For example, you could use this sentence in a business report to describe a meeting that was held between three parties to discuss a joint venture: "The meeting focused on establishing a framework for collaboration between the three partners."
Exact(9)
But given their respective track records, any collaboration between the three will be hotly anticipated.
One hundred and seven documents is the outcome of collaboration between the three Maghrebin countries and France.
Such factors seem to have discouraged collaboration between the three institutional spheres of the Triple Helix dynamics (Park and Leydesdorff 2010).
This finding is a result of the significant contribution of three Maghrebin countries: Morocco, Tunisia, and Algeria in association with the strong international collaboration between the three countries and France.
Among the 15 West African Member States, 6 has no industrial output; over the remaining, 2 (Ghana and Nigeria) exhibit relationships between the industry and government on the one hand and the industry and university on the other hand, but the joint collaboration between the three actors occurs only in Nigeria.
The major strength of this study is its large sample size, resulting from collaboration between the three Scandinavian countries.
Similar(51)
To summarize the collaboration between the nine actors; it appears that some collaborated more, and strong links were developed, while others had weaker links.
Thus began the final period of collaboration between the two.
Not so with Hamilton, which has seen close collaboration between the two inhabitants of the role.
When the talks began in 1999, collaboration between the two institutions was proposed.
Yet there has been too little collaboration between the two systems to solve their mutual problems.
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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