Meetup summary

2024-09-13 - Invitation to Analytic Combinatorics

Recommended reading:

• Analytic Combinatorics (hereby referred to as AC) by Flajolet and Sedgewick, sections I.1 and I.2. You may want to read through the preface and “invitation” sections, but be advised that the latter is a whirlwind tour and you will likely not pick up much of what’s being said until you get further into the book. This is intended more to whet your appetite.
• Check out the textbook website and download the book.

Agenda:

• Define combinatorial classes describe their connection to generating functions.
• Define the “analytic method” (as compared to “classical” methods) of combinatorics.
• Go over some basic combinatorial class and set notation and operations.
• Work some small examples to get a feel for how exactly the dummy variable “marks the size” of objects in a combinatorial class.
• Derive the “admissible constructions” for ordinary generating functions (unlabeled structures). (This is Theorem I.1 in the book.)