The best replacement for row_number is rank.

The best alternatives to row_number are rated as following:
★★★★★  rank
★★★★★  rownum
★★★★  dense_rank
★★★★  rank oracle
★★★  dense_rank sql server
★  rank tsql
★  dense_rank oracle

Your alternative for row_number is not listed? Suggest!
Speaking about row_number, one probably shouldn't forget about cte.

Other search terms related to row_number and their ratings are:
★★★★★ cte
You have in mind a companion for row_number and it is not yet here? Propose!



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row_number
rank
rownum