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pro vyhledávání: '"Pournin, Lionel"'
Autor:
Pournin, Lionel
Consider a non-negative number $t$ and a hyperplane $H$ of $\mathbb{R}^d$ whose distance to the center of the hypercube $[0,1]^d$ is $t$. If $t$ is equal to $0$ and $H$ is orthogonal to a diagonal of $[0,1]^d$, it is known that the $(d-1)$-dimensiona
Externí odkaz:
http://arxiv.org/abs/2407.04637
Autor:
Cardinal, Jean, Pournin, Lionel
The expansion of a polytope is an important parameter for the analysis of the random walks on its graph. A conjecture of Mihai and Vazirani states that all $0/1$-polytopes have expansion at least 1. We show that the generalization to half-integral po
Externí odkaz:
http://arxiv.org/abs/2402.14343
Autor:
Parlier, Hugo, Pournin, Lionel
Given a surface $\Sigma$ equipped with a set $P$ of marked points, we consider the triangulations of $\Sigma$ with vertex set $P$. The flip-graph of $\Sigma$ whose vertices are these triangulations, and whose edges correspond to flipping arcs appears
Externí odkaz:
http://arxiv.org/abs/2308.05688
Autor:
Buffière, Théophile, Pournin, Lionel
A $3$-dimensional polytope $P$ is $k$-equiprojective when the projection of $P$ along any line that is not parallel to a facet of $P$ is a polygon with $k$ vertices. In 1968, Geoffrey Shephard asked for a description of all equiprojective polytopes.
Externí odkaz:
http://arxiv.org/abs/2307.11366
Publikováno v:
SIAM J. Discrete Math. 38(4), 2643-2664 (2024)
We investigate the following question: how close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimiz
Externí odkaz:
http://arxiv.org/abs/2305.18597
The associahedron $\mathcal{A}(G)$ of a graph $G$ has the property that its vertices can be thought of as the search trees on $G$ and its edges as the rotations between two search trees. If $G$ is a simple path, then $\mathcal{A}(G)$ is the usual ass
Externí odkaz:
http://arxiv.org/abs/2211.07984
We propose a computational, convex hull free framework that takes advantage of the combinatorial structure of a zonotope, as for example its symmetry group, to orbitwise generate all canonical representatives of its vertices. We illustrate the propos
Externí odkaz:
http://arxiv.org/abs/2205.13309
Publikováno v:
Oper. Res. Lett. 52, 107057 (2024)
Geometric scaling, introduced by Schulz and Weismantel in 2002, solves the integer optimization problem $\max \{c\mathord{\cdot}x: x \in P \cap \mathbb Z^n\}$ by means of primal augmentations, where $P \subset \mathbb R^n$ is a polytope. We restrict
Externí odkaz:
http://arxiv.org/abs/2205.04063
Autor:
Pournin, Lionel
Publikováno v:
J. Anal. Math. 152(2), 557-594 (2024)
Consider the hyperplanes at a fixed distance $t$ from the center of the hypercube $[0,1]^d$. Significant attention has been given to determining the hyperplanes $H$ among these such that the $(d-1)$-dimensional volume of $H\cap[0,1]^d$ is maximal or
Externí odkaz:
http://arxiv.org/abs/2203.15054
Publikováno v:
In European Journal of Combinatorics May 2024 118