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The command used to edit quotas for a user and specify grace periods is `edquota -u -t`. This command is specifically designed to set user quotas, and with the `-t` option, it allows the administrator to define grace periods for the user. A grace period is a duration during which a user is allowed to exceed the set quota limits before any penalties are enforced.

When quotas are exceeded, the grace period gives the user time to address the issue without immediately facing restrictions or penalties for using more disk space than allocated. This is particularly useful in managing resources fairly while still allowing users some flexibility.

The `edquota` command facilitates changes to both soft and hard limits, and including the `-t` option enhances its functionality by enabling administrators to specify how long a user can go over their allocated quota before action is taken.

Other commands listed serve different purposes. For instance, `repquota -g` retrieves and displays quotas in a summarized format for groups but does not allow for editing. Similarly, `quota -g` shows the quota information for groups, and using `edquota -u` alone will enable editing user quotas but will not include options for managing grace periods. Thus, `edquota -u -t`