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Identifiability of Phylogenetic Level-2 Networks under the Jukes-Cantor Model

Englander AK, Frohn M, Gross E, Holtgrefe N, van Iersel L, Jones M, Sullivant S.   +6 more
europepmc   +1 more source

Poset resolutions and lattice-linear monomial ideals [PDF]

Journal of Algebra, 2010
We introduce the class of lattice-linear monomial ideals and use the lcm-lattice to give an explicit construction for their minimal free resolution. The class of lattice-linear ideals includes (among others) the class of monomial ideals with a linear ...
Timothy B P Clark
exaly   +2 more sources

On the Hilbert series of monomial ideals

Journal of Combinatorial Theory - Series A, 2013
AbstractTo every squarefree monomial ideal one can associate a hypergraph. In this paper we show that the Hilbert series of a squarefree monomial ideal can be obtained from the so-called edge induced polynomial of the associated hypergraph.
Afshin Goodarzi
exaly   +3 more sources

Transversal intersection of monomial ideals [PDF]

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2019
arXiv admin note: text overlap with arXiv:1611 ...
Indranath Sengupta
exaly   +3 more sources

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Combinatorial decompositions for monomial ideals

Journal of Symbolic Computation, 2021
The concept of involutive division has been introduced first in the works of \textit{Ch. Riquier} [Les systèmes d'équations aux dérivées partielles. Paris: Gauthier-Villars (1909; JFM 40.0411.01)] and \textit{M. Janet} [Leçons sur les systèmes d'équations aux dérivées partielles. Paris: Gauthier-Villars (1929; JFM 55.0276.01)].
openaire   +3 more sources

k-Decomposable Monomial Ideals

Algebra Colloquium, 2015
In this paper we introduce a class of monomial ideals, called k-decomposable ideals. It is shown that the class of k-decomposable ideals is contained in the class of monomial ideals with linear quotients, and when k is large enough, the class of k-decomposable ideals is equal to the class of ideals with linear quotients. In addition, it is shown that a
Rahmati-Asghar, Rahim, Yassemi, Siamak
openaire   +1 more source

Monomial ideals

Journal of Mathematical Sciences, 2007
The author studies the numerical characteristics of monomial ideals in polynomial rings \(A=k[x_1,\ldots x_n]\) and in exterior algebras \(E\) on the same number of variables. In Chapter 2 of the paper, the author generalizes Macaulay's theorem to quotient rings. That is, the author gives conditions on and ideal \(I\) and on ideals \(J\) containing \(I\
openaire   +2 more sources

Irreducible decomposition of monomial ideals

ACM SIGSAM Bulletin, 2005
In this paper we present two algorithms for irreducible decomposition of monomial ideals. We first use staircase structures to study the monomial ideals. We generalize the shifting degrees rule from two variables to three variables and then arbitrary case.
Shuhong Gao, Mingfu Zhu
openaire   +2 more sources

Circulant Digraphs and Monomial Ideals

2005
It is known that there exists a Minimum Distance Diagram (MDD) for circulant digraphs of degree two (or double-loop computer networks) which is an L-shape. Its description provides the graph's diameter and average distance on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by ...
Domingo Gómez-Pérez, Jaime Gutierrez 0001, Álvar Ibeas   +2 more
openaire   +1 more source

Regularity of Sn-invariant monomial ideals

Journal of Combinatorial Theory - Series A, 2021
Claudiu Raicu
exaly