# How could I use “respectively” to state three actions by subsets of four people?

For a scientific paper, I need to write these sentences as one sentence using "respectively".

Arnold and Benson [1] proved the claim when X is a rainbow set.

Carlson [2] proved the claim when X is a cloudy set.

Arnold and Davison [3] proved the claim when X is a rainy set.

My first attempt:

When X is a rainbow set, a cloudy set, and a rainy set, the claim was proved by Arnold and Benson [1], Carlson [2], and Arnold and Davison [3], respectively.

However, I am worried this might be ambiguous because there are more people than types of sets and the additional "and"s complicate the list. (Note: Arnold is the co-author of two papers.)

Is my attempt sound, and are there better ways to write this?

• Constructions with respectively tend to be awkward, because they often force people to rearrange the information to link it up in a more useful way: if you think people are going to be interested in who said what, then "respectively" is not the solution. On the other hand if you are forced to present the names for completeness (it is necessary to reference every single claim in your paper) and you don't think people actually care who said what, then do something like you said, and anyone who really cares will just have to disentangle it. – Stuart F Jan 20 at 16:38
• You introduce a logical problem with the word 'and': "and a rainy set." That's the seed of confusion. Your claim proofs are individual proofs. – Yosef Baskin Jan 20 at 17:59

This may be a case where the ampersand is useful. It may be used to combine two or more items to a composite singular noun. For example, "Smith & Nephew" is a pharmaceutical company.

Smith & Nephew plc, also known as Smith+Nephew, is a British multinational medical equipment manufacturing company headquartered in Watford, England.

Wikipedia

David Speaker identifies the ampersand as acceptable:

inside graphic or document tables or within parentheses when space is limited; in common shorthand expressions such as “rock & roll”; within a series to identify an item as part of its name and not a separator (e.g., “rock, pop, rhythm & blues, and hip-hop”);

and in identifying more than one addressee, particularly a couple: “Mr. & Mrs. Johnson.”

Grammar Book

Your sentence is thus easily modified to put the three sets of authors into one-to-one registration with their proofs:

When X is a rainbow set, a cloudy set, and a rainy set, the claim was proved by Arnold & Benson [1], Carlson [2], and Arnold & Davison [3], respectively.

If your aim is accuracy, I think you may need two independent clauses since the teams of Arnold + Benson and Arnold + Davidson proved two claims but not three while Carlson proved only one. How about:

When X is a rainbow set or a rainy set, the claim was proved by Arnold and Benson and Arnold and Davidson, respectively; Carlson further proved the claim when X is a cloudy set.

This construction removes the ambiguity inherent with your version. The word respectively makes more sense when the number of researchers matches the number of claims or proofs, as in my first clause.

• What about Benson? – niamulbengali Jan 20 at 16:26
• My mistake! I shall edit my answer. – RobJarvis Jan 20 at 16:27
• I don't understand your reasoning: How would you do if the three teams had, say, n_1, n_2, n_3 people each; with possible non-empty intersections between the teams? Also, isn't "Arnold and Benson and Arnold and Davidson" lacking at least one comma? I would say: "When X is a rainbow set, (comma) or a rainy set, the claim was proved by Arnold and Benson, (comma) and Arnold and Davidson, respectively;" – dache1771 Jan 20 at 16:44
• OK, @dache1771, if we were to modify the example to add more people to the teams, we might write: "When X is a rainbow set or a rainy set, the claim was proved by Arnold, and Arnold and Rainey, respectively; Carlson, Benson, and Hillard further proved the claim when X is a cloudy set." A comma may help to distinguish, for example, one researcher from the following team of more than one. I did not include a comma in my answer between "Arnold and Benson and Arnold and Davidson" primarily because Arnold appears as the first name in each team, thus removing any ambiguity. – RobJarvis Jan 20 at 18:40
• I see. However I think that Anton's answer is more general, it works with any number of teams and people for team – dache1771 Jan 21 at 7:39