A Natural Family of Flag Matroids

@article{Mier2007ANF,
  title={A Natural Family of Flag Matroids},
  author={Anna de Mier},
  journal={SIAM J. Discret. Math.},
  year={2007},
  volume={21},
  pages={130-140}
}
  • A. Mier
  • Published 29 September 2006
  • Mathematics
  • SIAM J. Discret. Math.
A flag matroid can be viewed as a chain of matroids linked by quotients. Flag matroids, of which relatively few interesting families have previously been known, are a particular class of Coxeter matroids. In this paper we give a family of flag matroids arising from an enumeration problem that is a generalization of the tennis ball problem. These flag matroids can also be defined in terms of lattice paths, and they provide a generalization of the lattice path matroids of [J. Bonin, A. de Mier… 

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References

SHOWING 1-10 OF 11 REFERENCES
Lattice path matroids: Structural properties
A linking polynomial of two matroids
The lattice of flats and its underlying flag matroid polytope
LetM be a matroid andF the collection of all linear orderings of bases ofM, orflags ofM. We define the flag matroid polytope Δ(F). We determine when two vertices of Δ(F) are adjacent, and provide a
Lattice path matroids: enumerative aspects and Tutte polynomials
A solution to the tennis ball problem
Gaussian, Strong and Transversal Greedoids
TLDR
The main purpose of this short paper is to prove directly that the two structures are identical, thus giving a simple axiomatic characterisation of the Gauss greedoids.
Enumerative combinatorics
TLDR
This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.
Progress in mathematics
Over four decades David Vogan’s groundbreaking work in representation theory has changed the face of the subject. We give a brief summary here.
Europ. J. Combinatorics
  • Europ. J. Combinatorics
  • 1999
...
...