Related papers: Bruhat Order on Partial Fixed Point Free Involutio…

In this paper we provide a preliminary investigation of subclasses of bounded posets with antitone involution which are "pastings" of their maximal Kleene sub-lattices. Specifically, we introduce super-paraorthomodular lattices, namely…

We study when blowup algebras are $F$-split or strongly $F$-regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals…

In this paper we consider the rank generating function of a separable permutation $\pi$ in the weak Bruhat order on the two intervals $[\text{id}, \pi]$ and $[\pi, w_0]$, where $w_0 = n,(n-1),..., 1$. We show a surprising result that the…

We prove that the restriction of Bruhat order to noncrossing partitions in type $A_n$ for the Coxeter element $c=s_1s_2 ...s_n$ forms a distributive lattice isomorphic to the order ideals of the root poset ordered by inclusion. Motivated by…

For an untwisted affine Kac-Moody Lie algebra $\mathfrak{g}$ with Cartan and Borel subalgebras $\mathfrak{h} \subset \mathfrak{b} \subset \mathfrak{g}$, affine Demazure modules are certain $U(\mathfrak{b})$-submodules of the irreducible…

Let $A=K[a_1,\ldots,a_n]$ be a weighted $\mathbb{N}$-filtered solvable polynomial algebra with filtration $FA=\{ F_pA\}_{p\in\mathbb{N}}$, where solvable polynomial algebras are in the sense of (A. Kandri-Rody and V. Weispfenning,…

For a bounded and graded poset $P$, we show that if $P$ is EL-shellable, then so is its $t$-fold Segre power $P^{(t)}=P\circ \cdots \circ P$ ($t$ factors), as defined by Bj\"orner and Welker [J. Pure Appl. Algebra, 198(1-3), 43--55 (2005)].…

We consider a partially asymmetric exclusion process (PASEP) on a finite number of sites with open and directed boundary conditions. Its partition function was calculated by Blythe, Evans, Colaiori, and Essler. It is known to be a…

We study classes of Borel subsets of the real line $\mathbb{R}$ such as levels of the Borel hierarchy and the class of sets that are reducible to the set $\mathbb{Q}$ of rationals, endowed with the Wadge quasi-order of reducibility with…

Let S be a basic closed semi-algebraic set in R^n and P the corresponding preordering in R[X_1,...,X_n]. We examine for which polynomials f there exist identities f+\ep q \in P for all \ep>0. These are precisely the elements of the…

Special partial matchings (SPMs) are a generalisation of Brenti's special matchings. Let a \emph{pircon} be a poset in which every non-trivial principal order ideal is finite and admits an SPM. Thus pircons generalise Marietti's zircons. We…

We prove that the rank polynomial of the lattice of order ideals of a loop fence poset is unimodal. This poset arises as the poset of join-irreducibles in the lattice of good matchings of loop graphs associated with notched arcs.…

Let alpha = (a,b,...) be a composition. Consider the associated poset F(alpha), called a fence, whose covering relations are x_1 < x_2 < ... < x_{a+1} > x_{a+2} > ... > x_{a+b+1} < x_{a+b+2} < ... . We study the associated distributive…

The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a…

A result of P\'olya states that every sequence of quadrature formulas $Q_n(f)$ with $n$ nodes and positive numbers converges to the integral $I(f)$ of a continuous function $f$ provided $Q_n(f)=I(f)$ for a space of algebraic polynomials of…

Bj\"orner and Wachs introduced CL-shellability as a technique for studying the topological structure of order complexes of partially ordered sets (posets). They also introduced the notion of recursive atom ordering, and they proved that a…

If $f\!:\![a,b]\to\R$ such that $f^{(n)}$ is integrable then integration by parts gives the formula \begin{align*} &\intab f(x)\,dx = &\frac{(-1)^n}{n!}\sum_{k=0}^{n-1}(-1)^{n-k-1}\left[ \phi_n^{(n-k-1)}(a)f^{(k)}(a)-…

A finite ranked poset is called a symmetric chain order if it can be written as a disjoint union of rank-symmetric, saturated chains. If $P$ is any symmetric chain order, we prove that $P^n/\mathbb{Z}_n$ is also a symmetric chain order,…

We discuss interrelations between: Cohn localizations of full square matrices; a Leavitt localization of a row; and the Jacobson quasi-inverses of quasi-regular elements. The latter Jacobson localizations appear naturally and easily in…

We study an effective one-dimensional (1D) orbital t-J model derived for strongly correlated e_g electrons in doped manganites. The ferromagnetic spin order at half filling is supported by orbital superexchange prop. to J which stabilizes…