ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (111)

[root@gaosheng ~]# mysql -uarcerzhang -parcerzhang -hlocalhost
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (111)
[root@gaosheng ~]# ll /var/lib/mysql/
total 20544
drwx------ 2 mysql mysql     4096 Apr  1 04:01 arcerdb
drwx------ 2 mysql mysql     4096 Mar 31 22:34 billy
-rw-rw---- 1 mysql mysql 10485760 Apr  1 03:56 ibdata1
-rw-rw---- 1 mysql mysql  5242880 Apr  1 03:56 ib_logfile0
-rw-rw---- 1 mysql mysql  5242880 Mar 30 23:07 ib_logfile1
drwx------ 2 mysql mysql     4096 Mar 31 23:32 meta
drwx------ 2 mysql mysql     4096 Mar 30 23:07 mysql
srwxrwxrwx 1 mysql mysql        0 Apr  1 03:56 mysql.sock
drwx------ 2 mysql mysql     4096 Mar 30 23:07 test
drwx------ 2 mysql mysql     4096 Mar 31 00:47 testdb
[root@gaosheng ~]# /etc/init.d/mysqld start
Starting MySQL:                                            [  OK  ]
[root@gaosheng ~]# mysql -uarcerzhang -parcerzhang
Welcome to the MySQL monitor.  Commands end with ; or g.
Your MySQL connection id is 2
Server version: 5.0.77-log Source distribution

Type 'help;' or 'h' for help. Type 'c' to clear the buffer.

mysql> show databases;
+--------------------+
| Database           |
+--------------------+
| information_schema | 
| arcerdb            | 
| billy              | 
| meta               | 
| mysql              | 
| test               | 
| testdb             | 
+--------------------+
7 rows in set (0.07 sec)

mysql>