Meetup summary

2025-10-17 - Labeled combinatorial structures - intro to exponential generating functions

Recommended reading:

• Analytic Combinatorics chapter II (labeled combinatorial structures). If possible, try to read up to and through Theorem II.1 (admissible constructions for labeled classes).

Agenda:

• Define labeled combinatorial classes and describe their connection to exponential generating functions (and touch on why they’re “exponential”). We’ll compare them directly with OGFs here and briefly touch on how certain problems which can be tortured into OGF form with great difficulty can be very easily expressed as EGFs.
• Go over some basic combinatorial class and set notation and operations.
• Work some small examples to get a feel for how EGFs work.
• Derive the “admissible constructions” for exponential generating functions (labeled structures). (This is Theorem II.1 in the book.)

We may cut some or all of this to watch the Mariners game. 🔱