MySQL variables open_files_limit, table_open_cache and max_connections are
inter-related, and this is for obvious reasons: all deal with file descriptors
one way or another.

If one of the value is provided but others are left out, mysqld calculates
others using a formula and in some cases, emits a warning if not possible.

The whole calculation behind obtaining the final file descriptor limit is a bit
byzantine and is as follows (for Linux):

EDIT: This applies to MySQL 5.5, in 5.6, as Daniël in comments pointed out,
few things have changed, check comment for details. I will probably make a
followup post on the differences.

1. First it tries to calculate a minimum requirement based on max_connections …

Before I get into details here is the bottom line. If you start MySQL on Solaris as a non-root (ie, mysql) user and for some reason you need to adjust the file descriptor resource limit for the parent shell, never use 'ulimit -n'. This will set both the soft and hard limit and may cause MySQL to adjust the max_connections and table_open_cache configuration variables upon next startup.

Use either:

 ulimit -S -n 1024

or something like:

prctl -n process.max-file-descriptor -t basic -v  1024 -r -i process $$

The Details

The default 'basic' privilege value for the resource control process.max-file-descriptor is 256. This control represents the soft ulimit for file descriptors per process. The default 'privileged' privilege is set to 65535, which represents the hard ulimit. A non-root user can adjust the soft limit down or up to the hard limit. Unless it has PRIV_SYS_RESOURCE a …

Before I get into details here is the bottom line. If you start MySQL on Solaris as a non-root (ie, mysql) user and for some reason you need to adjust the file descriptor resource limit for the parent shell, never use 'ulimit -n'. This will set both the soft and hard limit and may cause MySQL to adjust the max_connections and table_open_cache configuration variables upon next startup.

Use either:

 ulimit -S -n 1024

or something like:

prctl -n process.max-file-descriptor -t basic -v  1024 -r -i process $$

The Details

The default 'basic' privilege value for the resource control process.max-file-descriptor is 256. This control represents the soft ulimit for file descriptors per process. The default 'privileged' privilege is set to 65535, which represents the hard ulimit. A non-root user can adjust the soft limit down or up to the hard limit. Unless it has PRIV_SYS_RESOURCE a …

Before I get into details here is the bottom line. If you start MySQL on Solaris as a non-root (ie, mysql) user and for some reason you need to adjust the file descriptor resource limit for the parent shell, never use 'ulimit -n'. This will set both the soft and hard limit and may cause MySQL to adjust the max_connections and table_open_cache configuration variables upon next startup.

Use either:

 ulimit -S -n 1024

or something like:

prctl -n process.max-file-descriptor -t basic -v  1024 -r -i process $$

The Details

The default 'basic' privilege value for the resource control process.max-file-descriptor is 256. This control represents the soft ulimit for file descriptors per process. The default 'privileged' privilege is set to 65535, which represents the hard ulimit. A non-root user can adjust the soft limit down or up to the hard limit. Unless it has PRIV_SYS_RESOURCE a …