The fourth IPM biennial conference on combinatorics and computing (IPMCCC 2021) will be held on May 17-20, 2021. The conference is organized by the Combinatorics and Computing Group of IPM . The purpose of the IPMCCC is to bring together researchers interested in all areas of Combinatorics and Theoretical Computer Science, to discuss the latest developments and findings in their areas, take stock of what remains to be done and explore different visions for setting the direction for future work.