Postdoc extension talk
Speaker: Sucharita Biswas, IIT Bombay
Host: S Krishnan
Title: Classification of Wilf Equivalence and Shape Wilf Equivalence classes for POPs and Short Pattern Sets
Time, day and date: 10:30:00 AM - 11:30:00 AM, Monday, June 29
Venue: Ramanujan Hall
Abstract: Permutation pattern avoidance is a central topic in enumerative combinatorics. In this talk, I will discuss Wilf equivalence and shape Wilf equivalence for permutation patterns, with a particular focus on partially ordered patterns (POPs) and short pattern sets. Partially ordered patterns generalize the classical notion of permutation patterns by allowing certain entries of a pattern to be incomparable. I will present a complete Wilf equivalence classification of POPs of sizes $3$, $4$, and $5$ whose connected components are chains, thereby confirming a conjecture of Dimitrov posed during the problem session of the British Combinatorial Conference 2024 (BCC30). I will also describe recent results on shape Wilf equivalence for families of claw-shaped POPs. In particular, we prove that several such families are shape Wilf equivalent and obtain enumerative formulas for the corresponding avoidance classes.
Turning to short pattern sets, I will present a complete classification of shape Wilf equivalence classes for triples of patterns of length $3$. This work extends to a complete classification of quadruples and quintuples of patterns of length $3$, obtained in subsequent joint work. If time permits, I will conclude with a brief discussion of pattern avoidance in matchings, highlighting its rich connections with shape Wilf equivalence and related bijective phenomena.