Related papers: Subdivisions of lower Eulerian posets

In a companion paper, a canonical bijection was established between strong formal subdivisions of lower Eulerian posets and triples consisting of a lower Eulerian poset, a corresponding rank function, and a non-minimal element such that the…

In this paper we study finite Eulerian posets which are binomial, Sheffer or triangular. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as…

Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly, showing that the notion of $\cd$-index, long studied in…

Let $P$ be a finite partially ordered set. In a recent series of works, Proudfoot introduced the notion of $Z$-polynomials associated with $P$-kernels, providing a unified framework for various intersection cohomology Poincar\'e polynomials…

Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…

In this extended abstract we announce a proof that, in a Coxeter group of rank 3, low elements are in bijection with small inversion sets. This gives a partial confirmation of Conjecture 2 in [Dyer, Hohlweg '16]. That same article provides…

In this article we describe the Auslander-Reiten quiver for some posets with an involution, that we call types $\mathfrak{U}_n$ and $\mathfrak{U}_\infty$. These posets appear in the differentiation III of Zavadskij [12]. We follow the…

Viewing a fan as a partially ordered set (of cones) we consider a category of sheaves on the fan which corresponds to a category of equivariant sheaves on the corresponding toric variety if the fan is rational. In this category we define an…

To every poset P, Stanley (1986) associated two polytopes, the order polytope and the chain polytope, whose geometric properties reflect the combinatorial qualities of P. This construction allows for deep insights into combinatorics by way…

We introduce posets of simple vertex labeled minors of graphs and a generalization to the level of polymatroids, collectively termed minor posets. We show that any minor poset is isomorphic to the face poset of a regular CW sphere, and in…

We generalize the definition of the $cd$-index of an Eulerian poset to the class of semi-Eulerian posets. For simplicial semi-Eulerian Buchsbaum posets, we show that all coefficients of the $cd$-index are non-negative. This proves a…

The Eulerian idempotents, first introduced for the symmetric group and later extended to all reflection groups, generate a family of representations called the Eulerian representations that decompose the regular representation. In Type $A$,…

Let (X, O_X) be a noetherian formal scheme and consider D_qct(X) its derived category of sheaves with quasi-coherent torsion homology. We show that there is a bijection between the set of rigid (i.e. \tensor-ideals) localizing subcategories…

For any Coxeter system $(W,S)$ of rank $n$, we introduce an abstract boolean complex (simplicial poset) of dimension $2n-1$ that contains the Coxeter complex as a relative subcomplex. Faces are indexed by triples $(I,w,J)$, where $I$ and…

Let $f\colon M^{2n}\to\R^{2n+p}$, $2\leq p\leq n-1$, be an isometric immersion of a Kaehler manifold into Euclidean space. Yan and Zheng conjectured in \cite{YZ} that if the codimension is $p\leq 11$ then, along any connected component of…

It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the…

Classic mass partition results are about dividing the plane into regions that are equal with respect to one or more measures (masses). We introduce a new concept in which the notion of partition is replaced by that of a cover. In this case…

A new class of full fans in an euclidean space - tight fans - is introduced. Such fans are defined using a property of local symmetry in a face of a tiling. Tight fans are related to the theory of parallelotopes in an euclidean space. A…

The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…

In this paper, we study the semi-stable subcategories of the category of representations of a Euclidean quiver, and the possible intersections of these subcategories. Contrary to the Dynkin case, we find out that the intersection of…