The \(h\)-vectors of the edge rings of a special family of graphs. (English) Zbl 1540.13060
Summary: The \(h\)-vectors of homogeneous rings are one of the most important invariants that often reflect ring-theoretic properties. On the other hand, there are a few examples of edge rings of graphs whose \(h\)-vectors are explicitly computed. In this paper, we compute the \(h\)-vector of a special family of graphs, by using the technique of initial ideals and the associated simplicial complex.
MSC:
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 05E40 | Combinatorial aspects of commutative algebra |
| 13A70 | General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) |
| 13F55 | Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes |
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