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As I understand, single (sometimes) means one. For example, single pair of shoes or single parameter an so on. My question is can I use "a" with "single". For example,

This shows only a single type of correlation.

Is that correct? if not, then, why?

Thank you in advance for your help.

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Articles like "the" or "a" are used with nouns. "Single" is most commonly used an adjective, and is only a noun in a few limited contexts.

In your example, the noun is "type", and what matters is if whether you make it singular or plural, "type" or "types". The adjective "single" doesn't make any difference. Example:

This graph shows a single point of intersection between the two functions.

This graph shows multiple points of intersection between the two functions.

Naturally, it would be weird to say something like:

This graph shows a single points of ...

For general interest, here are a couple of examples using "single" as a noun:

The Beatles' song "Hey Jude" was first released as a single in 1968

It's not easy living as a single in the big city.

Late in the eighth inning the batter hit a lazy single to shallow right field, driving home the go-ahead run.

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    The question is a yes/no question. Unfortunately, the answer isn't very clear.
    – user2720402
    Commented May 14, 2021 at 7:02

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