https://re-st.github.io/blog/%EC%A1%B0%ED%95%A9%EB%A1%A0/ Recent content in 조합론 on Park, Geon (re-st) Hugo ko-kr Copyright © 2026, Geon Park. Fri, 01 May 2026 18:45:35 +0900 https://re-st.github.io/seminar/hall-algebra-of-the-category-of-matroids-eppolito-szczesny/ Thu, 26 Dec 2019 00:00:00 +0900 https://re-st.github.io/seminar/hall-algebra-of-the-category-of-matroids-eppolito-szczesny/ <blockquote> <p>Joint work: Chris Eppolito &amp; Matt Szczesny. 장소: KAIST E6-1 1401호</p> </blockquote> <h1 id="hall-algebra-of-the-category-of-matroids">Hall Algebra of the Category of Matroids</h1> <h2 id="1-hopf-algebra-배경">1. Hopf Algebra 배경</h2> <p>Combinatorial object + 연산 → Hopf algebra \(H\)</p> <p>구성 요소: multiplication \(m\), coproduct \(\Delta\), unit \(I\), counit \(\varepsilon\), antipode \(S\)</p> <p><strong>예시</strong>: \(G\) = 그래프 동형류의 집합 → monoid</p> $$H = k[G], \quad G \mapsto \sum_{T \subseteq V(G)} G_T \otimes G_{T}$$$$\varepsilon: H \to k, \quad G \mapsto \begin{cases} 1 & |V(G)| = 0 \\ 0 & \text{otherwise} \end{cases}$$<h2 id="2-combinatorial-results">2. Combinatorial Results</h2> <p><strong>예시 (w/ Miodrag Iovanov)</strong>:</p>