컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0200 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-22) Enumerative Combinatorics (SS-22) |
| 발표시간(Time) | 20th-D-13:30 -- 14:00 |
| 영문제목 (Title(Eng.)) |
Lattice-point enumeration, order polytopes, and generalized snake posets |
| 저자(Author(s)) |
Eon Lee1, Andrés R. Vindas Meléndez2, Zhi Wang3 GIST1, University of California Berkeley and Harvey Mudd College2, University of Science and Technology of China3 |
| 초록본문(Abstract) | Building from the work by von Bell et al.~(2022), we study the Ehrhart theory of the order polytopes arising from a special class of distributive lattices, known as generalized snake posets. We call the order polytopes of generalized snake posets, $\text{GSP}$s. We present arithmetic properties which the Ehrhart polynomials of $\text{GSP}$s satisfy, and compute their Gorenstein index. Then we give a combinatorial description of the chain polynomial of $\text{GSP}$s. We then shift our focus to the $h^*/f^*$-vectors of $\text{GSP}$s. In particular, we present an explicit formula of the $h^*$-polynomial for the two extremal cases of $\text{GSP}$s, namely the order polytopes from the ladder and regular snake posets. Then we provide a recursive formula for the $h^*$-polynomial of any $\text{GSP}$ and show that the $h^*/f^*$-vectors are entry-wise bounded by the $h^*/f^*$-vectors of the two extremal cases. The formulas we present involve several well-known families of combinatorial numbers such as, the Catalan, Pell, Delannoy and Narayana numbers. As corollaries to our results we prove basic combinatorial identities between these numbers. |
| 분류기호 (MSC number(s)) |
52B20 |
| 키워드(Keyword(s)) | Ehrhart theory, order polytope, generalized snake posets |
| 강연 형태 (Language of Session (Talk)) |
Korean |