Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Lionel Pournin"'
Publikováno v:
Contemporary mathematics
Contemporary mathematics, American Mathematical Society, 2021, Contemporary Mathematics, 764, pp.71-82. ⟨10.1090/conm/764/15336⟩
Contemporary mathematics, American Mathematical Society, 2021, Contemporary Mathematics, 764, pp.71-82. ⟨10.1090/conm/764/15336⟩
International audience
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::109398bb52eaa2f0a15700863b812778
https://doi.org/10.1090/conm/764/15336
https://doi.org/10.1090/conm/764/15336
Publikováno v:
Procedia Computer Science. 195:239-247
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eb73b2096c106be4c9516dec9a18008d
https://doi.org/10.1016/j.procs.2021.11.030
https://doi.org/10.1016/j.procs.2021.11.030
Autor:
Antoine Deza, Lionel Pournin
Publikováno v:
Computational Geometry
Computational Geometry, Elsevier, In press, 100, pp.101809. ⟨10.1016/j.comgeo.2021.101809⟩
Computational Geometry, Elsevier, In press, 100, pp.101809. ⟨10.1016/j.comgeo.2021.101809⟩
A class of counting problems ask for the number of regions of a central hyperplane arrangement. By duality, this is the same as counting the vertices of a zonotope. We give several efficient algorithms, based on a linear optimization oracle, that sol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::72104b1fbce4afaa1d539cfb26bdf7e8
https://hal.archives-ouvertes.fr/hal-03409685
https://hal.archives-ouvertes.fr/hal-03409685
Autor:
Lionel Pournin
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AS,..., Iss Proceedings (2013)
Consider the triangulations of a convex polygon with $n$ vertices. In 1988, Daniel Sleator, Robert Tarjan, and William Thurston have shown that the flip distance of two such triangulations is at most $2n-10$ when $n$ is greater than 12 and that this
Externí odkaz:
https://doaj.org/article/f7409619208b40959e4586921eb9d0f6
Publikováno v:
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2020, 148 (8), pp.3507-3516. ⟨10.1090/proc/14977⟩
Proceedings of the American Mathematical Society, American Mathematical Society, 2020, 148 (8), pp.3507-3516. ⟨10.1090/proc/14977⟩
We establish sharp asymptotic estimates for the diameter of primitive zonotopes when their dimension is fixed. We also prove that, for infinitely many integers $k$, the largest possible diameter of a lattice zonotope contained in the hypercube $[0,k]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::709e76d4f15330d4a026f7752f5ea69e
https://hal.archives-ouvertes.fr/hal-03409686/document
https://hal.archives-ouvertes.fr/hal-03409686/document
Publikováno v:
Optimization Letters
Optimization Letters, Springer Verlag, 2020, 14 (2), pp.309-326. ⟨10.1007/s11590-018-1338-7⟩
Optimization Letters, Springer Verlag, 2020, 14 (2), pp.309-326. ⟨10.1007/s11590-018-1338-7⟩
A lattice (d,k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers ranging between 0 and k. We consider the largest possible distance $$\delta $$(d,k) between two vertices in the edge-graph of a lattice (d,k)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::413264502224c7fa6875e4864104555f
https://hal.archives-ouvertes.fr/hal-03412184/file/ddgp_2018_OptL_HAL.pdf
https://hal.archives-ouvertes.fr/hal-03412184/file/ddgp_2018_OptL_HAL.pdf
Autor:
Lionel Pournin, Antoine Deza
Publikováno v:
Acta Mathematica Hungarica
Acta Mathematica Hungarica, Springer Verlag, In press, ⟨10.1007/s10474-017-0777-4⟩
Acta Mathematica Hungarica, Springer Verlag, In press, ⟨10.1007/s10474-017-0777-4⟩
We show that the largest possible diameter $\delta(d,k)$ of a $d$-dimensional polytope whose vertices have integer coordinates ranging between $0$ and $k$ is at most $kd-\lceil2d/3\rceil$ when $k\geq3$. In addition, we show that $\delta(4,3)=8$. This
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9eec4ccef033c76d0cefcb6a4e9edce5
https://doi.org/10.1007/s10474-017-0777-4
https://doi.org/10.1007/s10474-017-0777-4
Publikováno v:
Optimization Letters. 14:327-328
The erratum mostly concerns Table 4 and Figure 6 where two polytopes were misrepresented in the original version.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::412a959f7249bede6337cf26ef2c8b00
https://doi.org/10.1007/s11590-020-01534-x
https://doi.org/10.1007/s11590-020-01534-x
Publikováno v:
Discrete Applied Mathematics. 281:1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3f7b2ee2a184d0403f43e0f601dec53d
https://doi.org/10.1016/j.dam.2020.05.009
https://doi.org/10.1016/j.dam.2020.05.009
Publikováno v:
Journal of Combinatorial Theory, Series A. 172:105200
We introduce a graph structure on Euclidean polytopes. The vertices of this graph are the $d$-dimensional polytopes contained in $\mathbb{R}^d$ and its edges connect any two polytopes that can be obtained from one another by either inserting or delet
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2473d80712405e122a386167d743a8b8
https://doi.org/10.1016/j.jcta.2019.105200
https://doi.org/10.1016/j.jcta.2019.105200