Glicci simplicial complexes

One of the main open questions in liaison theory is whether every homogeneous Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for Stanley-Reisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Gorenstein complexes respectively. Moreover, we construct a simplicial complex which shows that the property of being glicci depends on the characteristic of the base field. As an application of our methods we establish new evidence for two conjectures of Stanley on partitionable complexes and on Stanley decompositions

Remarks on the existence of uniquely partitionable planar graphs

We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (D1,D1)-partitionable planar graphs with respect to the property D1 "to be a forest"

Geometric, Algebraic, and Topological Combinatorics

The 2019 Oberwolfach meeting "Geometric, Algebraic and Topological Combinatorics" was organized by Gil Kalai (Jerusalem), Isabella Novik (Seattle), Francisco Santos (Santander), and Volkmar Welker (Marburg). It covered a wide variety of aspects of Discrete Geometry, Algebraic Combinatorics with geometric flavor, and Topological Combinatorics. Some of the highlights of the conference included (1) Karim Adiprasito presented his very recent proof of the $g$-conjecture for spheres (as a talk and as a "Q\&A" evening session) (2) Federico Ardila gave an overview on "The geometry of matroids", including his recent extension with Denham and Huh of previous work of Adiprasito, Huh and Katz

La marche céleste: une marche oublieuse dans les subdivisions convexes à terminaison garantie

We present a new oblivious walking strategy for convex subdivisions. Our walk isfaster than the straight walk and more generally applicable than the visiblity walk. To provetermination of our walk we use a novel monotonically decreasing distance measure.Nous présentons une nouvelle stratégie de marche pour les subdivisions convexes.Cette stratégie est oublieuse, c’est à dire que la prochaine cellule visitée ne dépends pas des cellulesvisitées précédemment. Notre marche est plus rapide que la marche rectiligne et s’applique à dessubdivisions plus générales que la marche par visibilité. La démonstration de terminaison reposesur la décroissance monotone d’une nouvelle distance mesurant le progrès de la march

Celestial Walk: A Terminating, Memoryless Walk for Convex Subdivisions

International audienceA common solution for routing messages or performing point location in planar subdivisions consists in walking from one face to another using neighboring relationships. If the next face does not depend on the previously visited faces, the walk is called memoryless. We present a new memoryless strategy for convex subdivisions. The known alternatives are straight walk, which is a bit slower and not memoryless, and visibility walk, which is guaranteed to work properly only for Delaunay triangulations. We prove termination of our walk using a novel distance measure that, for our proposed walking strategy, is strictly monotonically decreasing