Cake cutting: Explicit examples for impossibility results

Autor: Guillaume Chèze

Publikováno v: Mathematical Social Sciences
Mathematical Social Sciences, Elsevier, 2019, 102, pp.68-72
Mathematical Social Sciences, 2019, 102, pp.68-72

International audience; In this article we suggest a model of computation for the cake cutting problem. In this model the mediator can ask the same queries as in the Robertson-Webb model but he or she can only perform algebraic operations as in the B

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::345a2edf254127e5c6458ce5aac182c0
https://doi.org/10.1016/j.mathsocsci.2019.09.005

On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems

Autor: Guillaume Chèze, Thomas Cluzeau

Publikováno v: Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics, Taylor & Francis, 2013, 20 (4), pp.475-479. ⟨10.1080/14029251.2013.868260⟩
Journal of Nonlinear Mathematical Physics, 2013, 20 (4), pp.475-479. ⟨10.1080/14029251.2013.868260⟩

International audience; We consider generalized Liénard polynomial differential systems. In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In this letter, we give a dir

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf58901d5ebe804536e0b47e41b0afdc
https://doi.org/10.1080/14029251.2013.868260

Bounding the number of remarkable values via Jouanolou's theorem

Autor: Guillaume Chèze

Publikováno v: Journal of Differential Equations
Journal of Differential Equations, 2015, ⟨10.1016/j.jde.2015.01.027⟩
Journal of Differential Equations, Elsevier, 2015, ⟨10.1016/j.jde.2015.01.027⟩

International audience; In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b48032ab4cf147838d70a40f16a05de7
https://doi.org/10.1016/j.jde.2015.01.027

Existence of a simple and equitable fair division: a short proof

Autor: Guillaume Chèze

Publikováno v: Mathematical Social Sciences
Mathematical Social Sciences, Elsevier, 2017, ⟨10.1016/j.mathsocsci.2017.03.006⟩
Mathematical Social Sciences, 2017, ⟨10.1016/j.mathsocsci.2017.03.006⟩

International audience; In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5827406122f606ff3b44a9b9b823ec2d
https://hal.archives-ouvertes.fr/hal-01492494

On the total order of reducibility of a pencil of algebraic plane curves

Autor: Guillaume Chèze, Laurent Busé

Publikováno v: Journal of Algebra
Journal of Algebra, Elsevier, 2011, 341 (1), pp.256-278. ⟨10.1016/j.jalgebra.2011.06.006⟩
Journal of Algebra, 2011, 341 (1), pp.256-278. ⟨10.1016/j.jalgebra.2011.06.006⟩

International audience; In this paper, the problem of bounding the number of reducible curves in a pencil of algebraic plane curves is addressed. Unlike most of the previous related works, each reducible curve of the pencil is here counted with its a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8cf923231a57344dc56ce469b9b5e284
https://doi.org/10.1016/j.jalgebra.2011.06.006