In this paper, we address the problem of determining an envy-free allocation of indivisible goods among multiple agents. EFX, which stands for envy-free up to any good, is a well-studied problem that has been shown to exist for specific scenarios, such as when there are only three agents with MMS valuations, as demonstrated by Chaudhury et al(2020), and for any number of agents when there are only two types of valuations as shown by Mahara(2020). Our contribution is to extend these results by showing that EFX exists for four agents with three distinct valuations. We further generalize this to show the existance of EFX allocations for n agents when n-2 of them have identical valuations.

The concepts in statistics and mathematics are the building blocks of the techniques and tools we use to gain deeper insights into structured and unstructured data. Statistical concepts lie at the heart of data science. In this informative session at SkillUp 2021, a two-day event organised by Analytics India Magazine, Rajeeva Karandikar of Chennai Mathematical Institute, presented a few examples (from history) to explain how to make the most of the available data and enormous computing power by combining statistical ideas with modern AI/ML tools. Rajeeva Karandikar is the Director at Chennai Mathematical Institute. He is a Fellow of the Indian Academy of Sciences and Indian National Science Academy.