arXiv Open Access 2016

Generalized multiplicities of edge ideals

Ali Alilooee Ivan Soprunov Javid Validashti

Lihat Sumber

Abstrak

We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show the $j$-multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the $j$-multiplicity of the edge ideal of a properly connected uniform hypergraph to the Hilbert-Samuel multiplicity of its special fiber ring. In addition, we provide general bounds for the generalized multiplicities of the edge ideals and compute these invariants for classes of uniform hypergraphs.

Topik & Kata Kunci

math.AC math.AG math.CO

Penulis (3)

Ali Alilooee

Ivan Soprunov

Javid Validashti

Format Sitasi

APA MLA BibTeX

Alilooee, A., Soprunov, I., Validashti, J. (2016). Generalized multiplicities of edge ideals. https://arxiv.org/abs/1607.00733

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2016
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓