| Title | : | Hierarchical Fractionally Intersecting Families |
| Speaker | : | Niranjan Balachandran (Math Dept., IIT-B) |
| Details | : | Wed, 7 Jun, 2023 4:00 PM @ CS15 |
| Abstract: | : | Suppose L ⊂ N0. A family F ⊂ P([n]) is said to be L-intersecting if for distinct A, B in F we have |A ∩ B| ∈ L. The problem of determining the size of a maximum L-intersecting family is a well-studied problem in extremal combinatorics which draws on ideas from several diverse toolkits, including the well-known Linear Algebra method. A more recent variant describes what one may call a fractional intersecting family when the set L consists of proper fractions of the form 0 < a b < 1. The problem of determining an optimal fractionally intersecting family is already nontrivial and open (up to a logarithmic factor). More recently, yet another variant called a Hierarchical fractionally intersecting family was introduced. We shall describe the motivation for studying this newer variant, and interestingly, in this case, the same extremal problem admits a very satisfactory answer. We shall describe these results in detail, and shall take a peek into the methods of proof. This is based on joint work with Srimanta Bhattacharya, Krishn Kher, Rogers Mathew, and Brahadeesh Sankarnarayanan. |
