MySQL InnoDB => composite PK and secondary index - mysql

Question

I understand that PK is part of every secondary index in InnoDB, but what about this situation:
I have table structure with two columns
a,b
I choose PK as a+b
and create INDEX on b
Question is, how looks structure on the secondary index ?
Is it stored as
b a
or
b a+b
Or another, more detailed example:
table: street , city , state , zip , fk_customers
PK: fk_customers + street + city + zip
INDEX (city)
INDEX (street)
Are the secondary indexes stored like this:
city fk_customers + street + zip
street fk_customers + city + zip
or like this:
city fk_customers + street + city + zip
street fk_customers + street + city + zip

Answer 1

That's easy to verify. My gut feeling told the secondary key on b would be b a b, but InnoDB is smart enough to omit the redundant b:
mysql> create table t1 (a varchar(32), b varchar(32), primary key (a,b));
mysql> alter table add index(b);
mysql> insert into t1 values('aaa','bbb');
Query OK, 1 row affected (0.00 sec)
Here's a hexdump of a secondary index page:
00004000 07 11 7d 29 00 00 00 04 ff ff ff ff ff ff ff ff |..})............|
00004010 00 00 00 00 ff ee cf d5 45 bf 00 00 00 00 00 00 |........E.......|
00004020 00 00 00 00 09 31 00 02 00 85 80 03 00 00 00 00 |.....1..........|
00004030 00 7f 00 05 00 00 00 01 00 00 00 00 00 01 e0 7e |...............~|
00004040 00 00 00 00 00 00 00 00 18 1a 00 00 09 31 00 00 |.............1..|
00004050 00 02 02 72 00 00 09 31 00 00 00 02 01 b2 01 00 |...r...1........|
00004060 02 00 1c 69 6e 66 69 6d 75 6d 00 02 00 0b 00 00 |...infimum......|
00004070 73 75 70 72 65 6d 75 6d 03 03 00 00 10 ff f1 62 |supremum.......b|
00004080 62 62 61 61 61 00 00 00 00 00 00 00 00 00 00 00 |bbaaa...........|
00004090 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
As you see, column a goes right after key column b. There is no trailing b

Answer 2

The answer above by akuzminsky is correct, but to add a bit more discussion: This is actually discussed in my blog post "The physical structure of records in InnoDB" under the heading "Secondary indexes":
For example, if a table has a PRIMARY KEY (a, b, c) and a secondary index KEY (a, d), the secondary key in the index will be as expected, (a, d) but the PKVs will contain only (b, c).
You can also confirm this by creating a table and using the page-dump or record-dump modes along with --trace to see the actual bytes encountered when reading the records