KCL2025.02

It is a triannual (three-times-a-year) seminar organized by academic genealogy from Professor Dongsu Kim in KAIST Combinatorics Laboratory, which KCL stands for. The aim of this seminar is to bring together active combinatorialists to discuss recent and prospective advances in algebraic and enumerative combinatorics and related areas. The style of talk tends to be less formal.

Program

• February 8

  • 13:30 - 14:00 Registration

  • 14:00 - 15:00 Invited Talk

    • Speaker Shishuo Fu, Chongqing University, China

    • Title A Combinatorially Refined View of Odd-Part Partitions with Designated Summands

    • Abstract In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called partitions with designated summands. These are constructed by taking unrestricted integer partitions and designating exactly one of each occurrence of a part. In the same work, they also considered the restricted partitions with designated summands wherein all parts must be odd.

  • 15:00 - 16:00 Invited Talk

    • Speaker Jang Soo Kim, Sungkyunkwan University

    • Title Enumeration of multiplex juggling card sequences using generalized q-derivatives

    • Abstract In 2019, Butler, Choi, Kim, and Seo introduced a new type of juggling card that represents multiplex juggling patterns in a natural bijective way. They conjectured a formula for the generating function for the number of multiplex juggling cards with capacity. In this paper we prove their conjecture. More generally, we find an explicit formula for the generating function with any capacity. We also find an expression for the generating function for multiplex juggling card sequences by introducing a generalization of the q-derivative operator. As a consequence, we show that this generating function is a rational function. This is joint work with Yumin Cho, Jaehyun Kim, and Nakyung Lee.

  • 16:00 - 16:30 Coffee Break

  • 16:30 - 17:00 Lightning Talks (5 minutes each)

  • 17:30 - 19:30 Dinner

Organizer

• Dongsu Kim, KAIST