Discrete Polymatroids
By Jürgen Herzog, Takayuki Hibi. 2002
58 citations recorded by the source corpus.
The discrete polymatroid is a multiset analogue of the matroid. Based on the polyhedral theory on integral polymatroids developed in late 1960's and in early 1970's, in the present paper the combinatorics and algebra on discrete polymatroids will be studied.
Subfields: Algebra and Number Theory, Signal Processing
View Paper: https://www.semanticscholar.org/paper/ba0c244e0cc8024f41074b1f930b1864f7020347
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In Algebra and Number Theory
- Adam Van Tuyl
- Takayuki Hibi
- Huy Tài Hà
- Jürgen Herzog
- Christopher A. Francisco
- Xinxian Zheng
- Rafael H. Villarreal
- Susan Morey
In Signal Processing
Citations in the corpus
- Ideals of fiber type and polymatroids (2005, unknown): “In the present paper we will continue our study on combinatorics and algebra of discrete polymatroids developed in the previous paper [9].”
- Sequentially Cohen-Macaulay edge ideals (2005, background): “lly generated by all squarefree monomials of degree n− 1, and hence I(Kn)∨ = I(Kn)∨ [n−1]. Now I(Kn) ∨ is a strongly stable squarefree monomial ideal (also a squarefree Veronese ideal in the sense of [8]). Hence I(Kn)∨ [n−1] has linear quotients if one orders the monomials in descending lexicographi”
- Monomial ideals whose powers have a linear resolution (2003, background): “roperty that all of its powers have a linear resolution. It is known [7] that polymatroidal ideals have linear resolutions and that powers of polymatroidal ideals are again polymatroidal (see [2] and [8]). In particular they have again linear resolutions. In general however, powers of ideals with li”