### Citations

144 |
Analyzing and modeling rank data
- Marden
- 1995
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Citation Context ...all functions f such that∑ i f(i, j) = ∑ k f(j, k) for all j). We thank S. Fiorini for bringing this fact to our attention. Second, these spaces arise in the context of the analysis of rank data, see =-=[5]-=-. There the R( n 2) is considered as the space of pairs and V1 is the space of means. They correspond to the Babington Smith Model resp. the Bradley/TerryMallows model. In Section 7.4.3 in [5], there ... |

24 |
Induced binary probabilities and the linear ordering polytope: A status report.
- Fishburn
- 1992
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Citation Context ... if pi(i) > pi(j) 0 if pi(i) < pi(j) The n-th Linear Ordering Polytope Pn is defined as the convex hull of the n! vectors ppi := (kij(pi))1≤i<j≤n ∈ R (n 2 ). In this we follow the definition given in =-=[4]-=-. The linear ordering polytope is an important and well-studied object in combinatorial optimization, see for example Chapter 6 of [6] and the references therein. For its study we will also consider t... |

13 | New facets of the linear ordering polytope
- Bolotashvili, Kovalev, et al.
- 1999
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Citation Context ... unique. We also note that the existence of the Z2 × Sn-action on Pn−1 is known from [2], where this action is constructed from the Z2 × Sn−1-action and a certain class of automorphisms borrowed from =-=[1]-=-. The projection Pn → Pn−1 maps n vertices to one. In [2, Lemma 2] the trivial and 3-cycle facets are shown to be the only facets having the maximal number of n!/2 vertices. Thus the preimages of thes... |

10 |
The Linear Ordering Problem. Exact and heuristic methods in combinatorial optimization
- Martí, Reinelt
- 2011
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Citation Context ...pi))1≤i<j≤n ∈ R (n 2 ). In this we follow the definition given in [4]. The linear ordering polytope is an important and well-studied object in combinatorial optimization, see for example Chapter 6 of =-=[6]-=- and the references therein. For its study we will also consider the n-th permutahedron; this is the polytope with n! vertices (pi(i))1≤i≤n ∈ R n for pi ∈ Sn. Both polytopes carry a natural Sn-action ... |

8 | Determining the automorphism group of the linear ordering polytope
- Fiorini
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Citation Context ... the decomposition arises from representation theoretic considerations in [7]. In that paper it is also shown to be unique. We also note that the existence of the Z2 × Sn-action on Pn−1 is known from =-=[2]-=-, where this action is constructed from the Z2 × Sn−1-action and a certain class of automorphisms borrowed from [1]. The projection Pn → Pn−1 maps n vertices to one. In [2, Lemma 2] the trivial and 3-... |

5 | The distance spectra of Cayley graphs of Coxeter groups - Renteln - 2011 |

2 |
Facets of linear signed order polytopes
- Fiorini, Fishburn
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Citation Context ... consider the other known families of facets (see for example [6]) from this point of view. The construction of the linear ordering polytope can be generalized to arbitrary finite Coxeter groups. See =-=[3]-=- for Type B and [7, Section 3.5] for the general case. There is still a decomposition into two invariant subspaces as in Theorem 1. The space V1 generalizes as expected: The action of the group is the... |

1 |
Spectra of Symmetrized Shuffling Operators, ArXiv e-prints arXiv:1102.2460
- Reiner, Saliola, et al.
- 2011
(Show Context)
Citation Context ...[5], there are also a basis of V1 and an generating set of V2 given. The later contains the basis we give in Section 3. Third, the decomposition arises from representation theoretic considerations in =-=[7]-=-. In that paper it is also shown to be unique. We also note that the existence of the Z2 × Sn-action on Pn−1 is known from [2], where this action is constructed from the Z2 × Sn−1-action and a certain... |