Combinatorial enumerations and Graycodeness on restricted growth functions avoiding vincular patterns
Speaker: Tran Thi Thu Huong

Time: 14h00, Thursday, July 2, 2020

Location: Room 507, Building A6

Abstract: The talk presents enumerations for restricted growth functions (RGFs) avoiding (i) single vincular pattern sets of length at most $3$ and (ii) two-pattern sets of a vincular pattern and a classic pattern of length at most $4$. The presented enumerations are counted by known classic sequences like Bell, Fibonacci, binary strings,etc. Moreover, we show a sufficient condition for the $3$-Graycodeness by the reflected Gray code order of RGFs avoiding a pattern set. Consequently, it allows us to prove the $3$-Graycodeness for some classes of RGFs avoiding particular pattern sets in (i) and (ii) by checking the condition satisfaction. This, in many cases, helps to reduce remarkably routine work for proving the $3$-Graycodeness on RGFs.