How do I find all the statistics and statistics columns on a specified object?

USE <database_name>;
GO
SELECT s.name AS statistics_name
    ,c.name AS column_name
    ,sc.stats_column_id
FROM sys.stats AS s
INNER JOIN sys.stats_columns AS sc
    ON s.object_id = sc.object_id AND s.stats_id = sc.stats_id
INNER JOIN sys.columns AS c
    ON sc.object_id = c.object_id AND c.column_id = sc.column_id
WHERE s.object_id = OBJECT_ID('<schema_name.object_name>');
GO

Make sure you have validated the schema_name and database_name before executing this code.