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KSIAM 2022 Spring Meeting
Friday, May 27, 2022 @ 1:20 PM - 5:40 PM KST
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KSIAM (Korean Society for Industrial and Applied Mathematics) will have the KSIAM 2022 Spring Conference at the Institute for Basic Science (IBS). Its academic session for Combinatorics decided to have an invited talk by Joonkyung Lee at the Hanyang University, a special session “Graph Theory” organized by Sang-il Oum and the IBS DIMAG, a special session “Enumerative Combinatorics” organized by Dongsu Kim at KAIST, and a poster session, all on May 27 afternoon. The deadline for the abstract submission is May 2 and the deadline for the early registration is May 9.
Invited talk (May 27 Friday, 16:40-17:40)
Joonkyung Lee이준경 (Hanyang University), Graph homomorphism inequalities and their applications
Counting (weighted) homomorphisms between graphs relates to a wide variety of areas, in- cluding graph theory, probability, statistical physics and theoretical computer science. In recent years, various new applications of inequalities between graph homomorphism counts have been found.
We will discuss some of the examples, including a simple proof of the Bondy–Simonovits theorem and a new estimate for the rainbow Turán numbers of even cycles. If time permits, we will also touch upon some recent progress on Sidorenko’s conjecture and related questions, in particular their applications on the bipartite Turán problems.
Based on joint work with David Conlon, Jaehoon Kim, Hong Liu, and Tuan Tran.
Special session “Graph Theory” (May 27, 13:20-14:40)
Organized by Sang-il Oum엄상일 (IBS Discrete Mathematics Group & KAIST).
Speakers
Boram Park박보람 (Ajou University), Odd Coloring of Graphs
An odd
We completely resolve Cranston’s conjecture. For
Joint work with Eun-Kyung Cho, Ilkyoo Choi, and Hyemin Kown.
Jongyook Park박종육 (Kyungpook National University), On the Delsarte bound
We study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence, we show that if a strongly regular graph contains a Delsarte clique, then the parameter μ is either small or large. Furthermore, we obtain a cubic polynomial that assures that a maximal clique in an amply regular graph is either small or large (under certain assumptions). Combining this cubic polynomial with the claw-bound, we rule out an infinite family of feasible parameters (v, k, λ, μ) for strongly regular graphs. Lastly, we provide tables of parameters (v, k, λ, μ) for nonexistent strongly regular graphs with smallest eigenvalue −4,−5,−6 or −7. This is joint work with Gary Greaves and Jack Koolen.
O-joung Kwon권오정 (Hanyang University and IBS Discrete Mathematics Group), Well-partitioned chordal graphs
We introduce a new subclass of chordal graphs that generalizes the class of split graphs, which we call well-partitioned chordal graphs. A connected graph
We observe that there are problems, for instance Densest
Stijn Cambie (IBS Extremal Combinatorics and Probability Group), Regular Cereceda’s Conjecture
The reconfiguration graph
This is based on joint work with Wouter Cames van Batenburg (TU Delft, the Netherlands) and Daniel Cranston (Virginia Commonwealth University, USA), which originates from the online workshop Graph Reconfiguration of the Sparse Graphs Coalition.
Special session “Enumerative Combinatorics” (May 27, 15:00-16:20)
Organized by Dongsu Kim김동수 (KAIST).
Speakers
Meesue Yoo류미수 (Chungbuk National University), Combinatorial description for the Hall-Littlewood expansion of unicellular LLT and chromatic quasisymmetric polynomials
In this work, we obtain a Hall–Littlewood expansion of the chromatic quasisymmetric functions by using a Dyck path model and linked rook placements. By using the Carlsson–Mellit relation between the chromatic quasisymmetric functions and the unicellular LLT polynomials, this combinatorial description for the Hall–Littlewood coefficients of the chromatic quasisymmetric functions also gives the coefficients of the unicellular LLT polynomials expanded in terms of the modified transformed Hall–Littlewood polynomials. Joint work with Seung Jin Lee.
Donghyun Kim김동현 (Sungkyunkwan University), Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials
The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable
Jisun Huh허지선 (Ajou University), Combinatorics on bounded Motzkin paths and its applications
A free Motzkin path of length
This is joint work with Hyunsoo Cho, Hayan Nam, and Jaebum Sohn.
Jihyeug Jang장지혁 (Sungkyunkwan University), A combinatorial model for the transition matrix between the Specht and web bases
We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition between the Specht and web bases, which answers Rhoades’s question. Furthermore, we study enumerative properties of these permutations. Joint work with Byung-Hak Hwang and Jaeseong Oh.