Related papers: Flag f-vectors of three-colored complexes
The aim of this paper is to classify all invariant generalized complex structure on a partial flag manifold $\mathbb{F}_\Theta$ with at most four isotropy summands. To classify them all we proved that an invariant generalized almost complex…
As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this…
We consider germs of holomorphic vector fields at the origin of $\mathbb{C}^3$, with non-isolated singularities that are tangent to a holomorphic foliation of codimension one. This configuration is known as a $2$-flag of foliations. The…
Surfaces with concentric $K$-contours and parallel $K$-contours in Euclidean $3$-space are defined. Crucial examples are presented and characterization of them are given.
The set of f-vectors of pure simplicial complexes is an important but little understood object in combinatorics and combinatorial commutative algebra. Unfortunately, its explicit characterization appears to be a virtually intractable…
We compute higher Frobenius-Schur indicators of pq-dimensional pointed Hopf algebras in characteristic p through their associated graded Hopf algebras. These indicators are gauge invariants for the monoidal categories of representations of…
In this paper we study invariant almost Hermitian geometry on generalized flag manifolds which the isotropy representation decompose into two or three irreducible components. We will provide a classification of such flag manifolds admitting…
Let $f_s: X_s \to {\bf {P}}^2$ be the blowing-up of $s$ distinct points and $E$ a vector bundle on $X_s$. Here we give a cohomological criterio which is equivalent to $E \cong f_s^\ast (A)$ with $A$ a direct sum of line bundles. We also…
We study the index of symmetry of a compact generalized flag manifold M=G/H endowed with an invariant Kaehler structure. When the group G is simple we show that the leaves of symmetry are irreducible Hermitian symmetric spaces and we…
In this paper, we present a new method for computing the f-vector of a marked order polytope. Namely, given an arbitrary (polyhedral) subdivision of an arbitrary convex polytope, we construct a cochain complex (over the two-element field…
Let $\mathbb{K}[G]$ be the edge ring of a finite simple graph $G$. Investigating properties of the $h$-vector of $\mathbb{K}[G]$ is of great interest in combinatorial commutative algebra. However, there are few families of graphs for which…
A generalization of a theorem of Crabb and Hubbuck concerning the embedding of flag representations in divided powers is given, working over an arbitrary finite field F, using the category of functors from finite-dimensional F-vector spaces…
A Gelfand-Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent description of the face structure of a GC-polytope in terms of so…
We describe the torus-equivariant cohomology of weighted partial flag orbifolds ${\mathrm{w}}\Sigma$ of type $A$. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to…
We characterise graphs that have three distinct eigenvalues and coherent ranks 8 and 9, linking the former to certain symmetric 2-designs and the latter to specific quasi-symmetric 2-designs. This characterisation leads to the discovery of…
In 1970, Walkup completely described the set of $f$-vectors for the four 3-manifolds $S^3$, $S^2 twist S^1$, $S^2 \times S^1$, and $RP^3$. We improve one of Walkup's main restricting inequalities on the set of $f$-vectors of 3-manifolds. As…
We study the properties of coloured three particle s-wave quark clusters when flavour symmetry is broken. The relevance of such clusters for models of pentaquarks is shortly mentioned.
One describes, using a detailed analysis of Atiyah--Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This…
We introduce new classes of integrable models that exhibit a structure similar to that of flag vector spaces. We present their Hamiltonians, R-matrices and Bethe-ansatz solutions. These models have a new type of generalized graded algebra…
The paper investigates connections between abstract polytopes and properly edge colored graphs. Given any finite n-edge-colored n-regular graph G, we associate to G a simple abstract polytope P_G of rank n, called the colorful polytope of…