<partition_by_clause>

Divides the result set produced by the FROM clause into partitions to which the ROW_NUMBER function is applied. For the PARTITION BY syntax, see OVER Clause (Transact-SQL).

<order_by_clause>

Determines the order in which the ROW_NUMBER value is assigned to the rows in a partition. For more information, see ORDER BY Clause (Transact-SQL). An integer cannot represent a column when the <order_by_clause> is used in a ranking function.

bigint

The ORDER BY clause determines the sequence in which the rows are assigned their unique ROW_NUMBER within a specified partition.

A. Returning the row number for salespeople

SELECT FirstName, LastName, ROW_NUMBER() OVER(ORDER BY SalesYTD DESC) AS 'Row Number', SalesYTD, PostalCode 

FROM Sales.vSalesPerson

WHERE TerritoryName IS NOT NULL AND SalesYTD <> 0;

B. Returning a subset of rows

USE AdventureWorks;
GO
WITH OrderedOrders AS
(
    SELECT SalesOrderID, OrderDate,
    ROW_NUMBER() OVER (ORDER BY OrderDate) AS 'RowNumber'
    FROM Sales.SalesOrderHeader 
) 
SELECT * 
FROM OrderedOrders 
WHERE RowNumber BETWEEN 50 AND 60;

C. Using ROW_NUMBER() with PARTITION

SELECT FirstName, LastName, ROW_NUMBER() OVER(PARTITION BY PostalCode ORDER BY SalesYTD DESC) AS 'Row Number', SalesYTD, PostalCode 
FROM Sales.vSalesPerson
WHERE TerritoryName IS NOT NULL AND SalesYTD <> 0;

Reference

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