Öz
In this paper,
we give a criterion of the Gorenstein property of
the Ehrhart ring of the stable set polytope of
an h-perfect graph:
the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if
(1)
sizes of maximal cliques are constant (say $n$) and
(2)
(a)
$n=1$,
(b)
$n=2$ and there is no odd cycle without chord and length at least 7 or
(c)
$n\geq 3$ and there is no odd cycle without chord and length at least 5.
Anahtar Kelimeler
Gorenstein ring h-perfect graph Ehrhart ring stable set polytope
Kaynakça
- W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1993.
- V. Chvatal, On certain polytopes associated with graphs, J. Combinatorial Theory Ser. B 18(2), (1975), 138-154.
- R. M. Fossum, The Divisor Class Group of a Krull Domain, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 74, Springer-Verlag, New York- Heidelberg, 1973.
- J. Herzog, T. Hibi and D. I. Stamate, The trace of the canonical module, Israel J. Math., 233(1) (2019), 133-165.
- T. Hibi and A. Tsuchiya, Odd cycles and Hilbert functions of their toric rings, Mathematics, 8(1) (2020), 22.
- M. Hochster, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials and polytopes, Ann. of Math., 96 (1972), 318-337.
- M. Miyazaki, On the canonical ideal of the Ehrhart ring of the chain polytope of a poset, J. Algebra, 541 (2020), 1-34.
- H. Ohsugi and T. Hibi, Special simplices and Gorenstein toric rings, J. Combin. Theory Ser. A, 113(4) (2006), 718-725.
- N. Sbihi and J.-P. Uhry, A class of h-perfect graphs, Discrete Math., 51(2) (1984), 191-205.
- R. P. Stanley, Hilbert functions of graded algebras, Advances in Math., 28(1) (1978), 57-83.
- R. P. Stanley, Two poset polytopes, Discrete Comput. Geom., 1(1) (1986), 9-23.
Öz
Kaynakça
- W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1993.
- V. Chvatal, On certain polytopes associated with graphs, J. Combinatorial Theory Ser. B 18(2), (1975), 138-154.
- R. M. Fossum, The Divisor Class Group of a Krull Domain, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 74, Springer-Verlag, New York- Heidelberg, 1973.
- J. Herzog, T. Hibi and D. I. Stamate, The trace of the canonical module, Israel J. Math., 233(1) (2019), 133-165.
- T. Hibi and A. Tsuchiya, Odd cycles and Hilbert functions of their toric rings, Mathematics, 8(1) (2020), 22.
- M. Hochster, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials and polytopes, Ann. of Math., 96 (1972), 318-337.
- M. Miyazaki, On the canonical ideal of the Ehrhart ring of the chain polytope of a poset, J. Algebra, 541 (2020), 1-34.
- H. Ohsugi and T. Hibi, Special simplices and Gorenstein toric rings, J. Combin. Theory Ser. A, 113(4) (2006), 718-725.
- N. Sbihi and J.-P. Uhry, A class of h-perfect graphs, Discrete Math., 51(2) (1984), 191-205.
- R. P. Stanley, Hilbert functions of graded algebras, Advances in Math., 28(1) (1978), 57-83.
- R. P. Stanley, Two poset polytopes, Discrete Comput. Geom., 1(1) (1986), 9-23.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 17 Temmuz 2021 |
| Yayımlandığı Sayı | Yıl 2021 |