Related papers: Brewing Fubini-Bruhat Orders
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumerative results for intersecting varieties defined by rank…
The paper examines a partial order on bipartite graphs (X1, X2, E) with n vertices, X1UX2={1,2,...,n}. This partial order is a natural partial order of subobjects of an object in a triangular category with bipartite graphs as morphisms.
There is a natural analogue of weak Bruhat order on the involutions in any Coxeter group. The saturated chains of intervals in this order correspond to reduced words for a certain set of group elements called atoms. Brion gives a general…
We give positive descriptions for certain Schubert structure constants $c_{u,v}^w$ for the full flag variety in Lie types $C$ and $D$. This is accomplished by first observing that a number of the $K=GL(n,\C)$-orbit closures on these flag…
The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arises from an amalgamation-with-predimension construction in the style of Hrushovski. The…
A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces are equipped with the Gromov-weak topology and give a new…
In this paper the solutions $u_{\nu}=u_{\nu}(x,t)$ to fractional diffusion equations of order $0<\nu \leq 2$ are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations…
Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of…
We characterise the permutations pi such that the elements in the closed lower Bruhat interval [id,pi] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the…
Let $s$ be West's deterministic stack-sorting map. A well-known result (West) is that any length $n$ permutation can be sorted with $n-1$ iterations of $s.$ In 2020, Defant introduced the notion of highly-sorted permutations -- permutations…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
We prove a criterion for the normality of Schubert varieties in twisted affine Grassmannians in terms of the order of the algebraic fundamental group of a certain Levi subgroup, in particular in small positive characteristic. As an…
The purpose of this paper is to establish a correspondence between the higher Bruhat orders of Yu. I. Manin and V. Schechtman, and the cup-$i$ coproducts defining Steenrod squares in cohomology. To any element of the higher Bruhat orders we…
The variety of complete quadrics is the wonderful compactification of $GL_n/O_n$ and admits a cell decomposition into Borel orbits indexed by combinatorial objects called $\mu$-involutions. We study Coxeter-theoretic properties of…
We establish counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form $x\_i-x\_j=s$ for some integer $s$. Classical…
It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of…
In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove formulas on enumeration of bigrassmannian permutations weakly…
The main purpose of this paper is to prove that the Bruhat-Chevalley ordering of the symmetric group when restricted to the fixed-point-free involutions forms an $EL$-shellable poset whose order complex triangulates a ball. Another purpose…
Restriction varieties in the orthogonal Grassmannian are subvarieties of $OG(k, n)$ defined by rank conditions given by a flag that is not necessarily isotropic with respect to the relevant symmetric bilinear form. In particular, Schubert…
We introduce a natural partial order in structurally natural finite subsets of the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling…