The tree representation of ∑n + 1

Robinson, Alan; Whitehouse, Sarah

doi:10.1016/0022-4049(95)00116-6

Cited by 67 publications

(80 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that this map is induced from a map of lattices, as the relevant lattice in ‫ޒ‬ ( n 2 ) is the index two sublattice of ‫ޚ‬ ( n 2 ) with even coordinate sum. The fact that is simplicial of dimension n − 3 is due to [Robinson and Whitehouse 1996]. Recall that a fan is smooth if for each cone the intersection of the lattice with the linear span of that cone is generated by the first lattice points on each ray of the cone.…”

Section: A Toric Variety Containing M 0nmentioning

confidence: 99%

Equations for Chow and Hilbert quotients

Gibney¹,

Maclagan

2010

ANT

View full text Add to dashboard Cite

We give explicit equations for the Chow and Hilbert quotients of a projective scheme X by the action of an algebraic torus T in an auxiliary toric variety. As a consequence we provide geometric invariant theory descriptions of these canonical quotients, and obtain other GIT quotients of X by variation of GIT quotient. We apply these results to find equations for the moduli space M 0,n of stable genus-zero n-pointed curves as a subvariety of a smooth toric variety defined via tropical methods.

show abstract

Section: A Toric Variety Containing M 0nmentioning

confidence: 99%

Equations for Chow and Hilbert quotients

Gibney¹,

Maclagan

2010

ANT

View full text Add to dashboard Cite

show abstract

“…Proof The proof is given in [8]. Suffice it to say here thatT n has an evident cubical structure, with the internal edge-lengths as cubical coordinates.…”

Section: Proposition 23mentioning

confidence: 99%

“…From [8] we recall topological properties of the space of n-trees, and prove a homeomorphism with the nerve of the lattice of partitions of the set {1, 2, . .…”

Section: The Space Of Fully-grown N-treesmentioning

confidence: 99%

See 1 more Smart Citation

Partition complexes, duality and integral tree representations

Robinson

2004

Algebr. Geom. Topol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This space has a natural stratification, with each cell corresponding to a combinatorial type of trees -this is the complex of phylogenetic trees. Complexes of trees were studied for different purposes, before and after [2], see [4,17,19,21,25,24]. In particular, in [21] Robinson and Whitehouse determined the homotopy type of the complex of phylogenetic trees on n leaves to be a wedge of (n − 1)!…”

mentioning

confidence: 99%

Nested set complexes of Dowling lattices and complexes of Dowling trees

Delucchi

2007

J Algebr Comb

View full text Add to dashboard Cite

Abstract. Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice Qn(G) (see [8]) and of its subposet of the G-symmetric partitions Q 0 n (G) which was recently introduced by Hultman in [20], together with the complex of Gsymmetric phylogenetic trees T G n . Hultman shows that the complexes T G n and e ∆(Q 0 n (G)) are homotopy equivalent and Cohen-Macaulay, and determines the rank of their top homology.An application of the theory of building sets and nested set complexes by Feichtner and Kozlov [12] shows that in fact T G n is subdivided by the order complex of Q 0 n (G). We introduce the complex of Dowling trees Tn(G) and prove that it is subdivided by the order complex of Qn(G) and contains T G n as a subcomplex. We show that Tn(G) is obtained from T G n by successive coning over certain subcomplexes. It is well known that Qn(G) is shellable, and of the same dimension as T G n . We explicitly and independently calculate how many homology spheres are added in passing from T G n to Tn(G).

show abstract

The tree representation of ∑n + 1

Cited by 67 publications

References 6 publications

Equations for Chow and Hilbert quotients

Equations for Chow and Hilbert quotients

Partition complexes, duality and integral tree representations

Nested set complexes of Dowling lattices and complexes of Dowling trees

Contact Info

Product

Resources

About