Gnu/coreutils/Conditional-Executability

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27.2.4 Conditional Executability

There is one more special type of symbolic permission: if you use ‘X’ instead of ‘x’, execute/search permission is affected only if the file is a directory or already had execute permission.

For example, this mode:

a+X

gives all users permission to search directories, or to execute files if anyone could execute them before.