我也会投票给Mosty Mostacho的解决方案，对他的查询代码进行了轻微的修改:

SELECT a.i, a.j, (
    SELECT count(*) from test b where a.j >= b.j AND a.i = b.i
) AS row_number FROM test a

会得到相同的结果:

+------+------+------------+
|    i |    j | row_number |
+------+------+------------+
|    1 |   11 |          1 |
|    1 |   12 |          2 |
|    1 |   13 |          3 |
|    2 |   21 |          1 |
|    2 |   22 |          2 |
|    2 |   23 |          3 |
|    3 |   31 |          1 |
|    3 |   32 |          2 |
|    3 |   33 |          3 |
|    4 |   14 |          1 |
+------+------+------------+

对于表格:

+------+------+
|    i |    j |
+------+------+
|    1 |   11 |
|    1 |   12 |
|    1 |   13 |
|    2 |   21 |
|    2 |   22 |
|    2 |   23 |
|    3 |   31 |
|    3 |   32 |
|    3 |   33 |
|    4 |   14 |
+------+------+

唯一的区别是查询不使用JOIN和GROUP BY，而是依赖于嵌套选择。

从MySQL 8.0.0及以上版本，您可以本机使用窗口函数。

1.4 MySQL 8.0的新特性:

窗口函数。 MySQL现在支持窗口函数，对于查询中的每一行，使用与该行相关的行执行计算。这些函数包括RANK()、LAG()和NTILE()。此外，一些现有的聚合函数现在可以用作窗口函数;例如SUM()和AVG()。

ROW_NUMBER() over_clause:

返回分区内当前行的编号。行号从1到分区行数。 ORDER BY影响行编号的顺序。没有ORDER BY，行编号是不确定的。

演示:

CREATE TABLE Table1(
  id INT AUTO_INCREMENT PRIMARY KEY, col1 INT,col2 INT, col3 TEXT);

INSERT INTO Table1(col1, col2, col3)
VALUES (1,1,'a'),(1,1,'b'),(1,1,'c'),
       (2,1,'x'),(2,1,'y'),(2,2,'z');

SELECT 
    col1, col2,col3,
    ROW_NUMBER() OVER (PARTITION BY col1, col2 ORDER BY col3 DESC) AS intRow
FROM Table1;

DBFiddle演示

我总是遵循这个模式。给定这个表格:

+------+------+
|    i |    j |
+------+------+
|    1 |   11 |
|    1 |   12 |
|    1 |   13 |
|    2 |   21 |
|    2 |   22 |
|    2 |   23 |
|    3 |   31 |
|    3 |   32 |
|    3 |   33 |
|    4 |   14 |
+------+------+

你可以得到这样的结果:

+------+------+------------+
|    i |    j | row_number |
+------+------+------------+
|    1 |   11 |          1 |
|    1 |   12 |          2 |
|    1 |   13 |          3 |
|    2 |   21 |          1 |
|    2 |   22 |          2 |
|    2 |   23 |          3 |
|    3 |   31 |          1 |
|    3 |   32 |          2 |
|    3 |   33 |          3 |
|    4 |   14 |          1 |
+------+------+------------+

通过运行这个不需要定义任何变量的查询:

SELECT a.i, a.j, count(*) as row_number FROM test a
JOIN test b ON a.i = b.i AND a.j >= b.j
GROUP BY a.i, a.j

看看这篇文章，它展示了如何在MySQL中使用分区by模拟SQL ROW_NUMBER()。我在WordPress实现中遇到了同样的场景。我需要ROW_NUMBER()，但它不在那里。

http://www.explodybits.com/2011/11/mysql-row-number/

本文中的示例使用了一个按字段划分的分区。要按额外的字段进行分区，你可以这样做:

  SELECT  @row_num := IF(@prev_value=concat_ws('',t.col1,t.col2),@row_num+1,1) AS RowNumber
         ,t.col1 
         ,t.col2
         ,t.Col3
         ,t.col4
         ,@prev_value := concat_ws('',t.col1,t.col2)
    FROM table1 t,
         (SELECT @row_num := 1) x,
         (SELECT @prev_value := '') y
   ORDER BY t.col1,t.col2,t.col3,t.col4 

使用concat_ws处理null。我使用int、date和varchar对3个字段进行了测试。希望这能有所帮助。查看这篇文章，因为它分解了这个查询并解释了它。

我没有看到任何简单的答案涵盖“PARTITION BY”部分，所以我的答案是:

SELECT
    *
FROM (
    select
        CASE WHEN @partitionBy_1 = l THEN @row_number:=@row_number+1 ELSE @row_number:=1 END AS i
        , @partitionBy_1:=l AS p
        , t.*
    from (
        select @row_number:=0,@partitionBy_1:=null
    ) as x
    cross join (
        select 1 as n, 'a' as l
        union all
        select 1 as n, 'b' as l    
        union all
        select 2 as n, 'b' as l    
        union all
        select 2 as n, 'a' as l
        union all
        select 3 as n, 'a' as l    
        union all    
        select 3 as n, 'b' as l    
    ) as t
    ORDER BY l, n
) AS X
where i > 1

The ORDER BY clause must reflect your ROW_NUMBER need. Thus there's already a clear limitation: you can't have several ROW_NUMBER "emulation" of this form at the same time. The order of the "computed column" matters. If you have mysql compute those column in another order, it might not work. In this simple example I only put one but you can have several "PARTITION BY" parts CASE WHEN @partitionBy_1 = part1 AND @partitionBy_2 = part2 [...] THEN @row_number:=@row_number+1 ELSE @row_number:=1 END AS i , @partitionBy_1:=part1 AS P1 , @partitionBy_2:=part2 AS P2 [...] FROM ( SELECT @row_number:=0,@partitionBy_1:=null,@partitionBy_2:=null[...] ) as x

在MySQL中没有像rownum, row_num()这样的函数，但方法如下:

select 
      @s:=@s+1 serial_no, 
      tbl.* 
from my_table tbl, (select @s:=0) as s;