Zobrazeno 1 - 10
of 121
pro vyhledávání: '"Floystad, Gunnar"'
Autor:
Fløystad, Gunnar, Manchon, Dominique
To a submodular function we define a class of preorders, conforming preorders. A submodular function $z$ corresponds to a generalized permutahedron $\Pi(z)$. We show the faces of $\Pi(z)$ are in bijection with the conforming preorders. The face poset
Externí odkaz:
http://arxiv.org/abs/2409.08200
Autor:
Fløystad, Gunnar
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite topologies,
Externí odkaz:
http://arxiv.org/abs/2309.01468
Autor:
Fløystad, Gunnar
We introduce new concepts and viewpoints on combinatorial Hopf species and algebras. We give a category ${\rm \bf set_{\mathbb{N}}}$ whose objects are sets, and (dualizable) morphisms represented by matrices of non-negative integers. For a bimonoid s
Externí odkaz:
http://arxiv.org/abs/2301.06479
Autor:
Fløystad, Gunnar, Mafi, Amir
We show that any polarization of an artin monomial ideal defines a triangulated ball. This proves a conjecture of A.Almousa, H.Lohne and the first author. Geometrically, polarizations of ideals containing $(x_1^{a_1}, \ldots, x_n^{a_n})$ define full-
Externí odkaz:
http://arxiv.org/abs/2212.09528
We consider the bialgebra of hypergraphs, a generalization of Schmitt's Hopf algebra of graphs, and show it has a cointeracting bialgebra. So one has a double bialgebra in the sense of L. Foissy, who recently proved there is then a unique double bial
Externí odkaz:
http://arxiv.org/abs/2212.03501
Autor:
Fløystad, Gunnar
For stacked simplicial complexes, (special subclasses of such are: trees, triangulations of polygons, stacked polytopes), we give an explicit bijection between partitions of facets (for trees: edges), and partitions of vertices into independent sets.
Externí odkaz:
http://arxiv.org/abs/2207.04444
Triangulations of polygons and stacked simplicial complexes: separating their Stanley-Reisner ideals
Autor:
Fløystad, Gunnar, Orlich, Milo
A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial complexes, in part
Externí odkaz:
http://arxiv.org/abs/2108.06520
Autor:
Fløystad, Gunnar
We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly stable ide
Externí odkaz:
http://arxiv.org/abs/2105.14604
Autor:
Fløystad, Gunnar
We consider profunctors $f : P \promap Q$ between posets and introduce their {\em graph} and {\em ascent}. The profunctors $\Pro(P,Q)$ form themselves a poset, and we consider a partition $\cI \sqcup \cF$ of this into a down-set $\cI$ and up-set $\cF
Externí odkaz:
http://arxiv.org/abs/2104.02767
We organize colored aromatic trees into a pre-Lie-Rinehart algebra (i.e. a flat torsion-free Lie-Rinehart algebra) endowed with a natural trace map, and show the freeness of this object among pre-Lie-Rinehart algebras with trace. This yields the alge
Externí odkaz:
http://arxiv.org/abs/2002.05718