Related papers: A note on the Bj\"{o}rner--Kalai theorem

We study the homological properties of $\Delta_{\mathbf{r}}(n_1, \dots, n_e)$, a simplicial complex formed by sequentially gluing complete graphs along $(r_i-1)$-simplices. This construction generates precisely the chordal clique complexes,…

The main purpose of this paper is to investigate the formal deficiency indices ${\cal N}_{\pm}(I)$ of a symmetric first order system $$ Jf'+Bf=\lambda {\cal H} f $$ on an interval $I$, where $I=\mathbb{R}$ or $I=\mathbb{R}_\pm.$ Here…

Classical simplicial cohomology on a simplicial complex G deals with functions on simplices x in G. Quadratic cohomology deals with functions on pairs of simplices (x,y) in G x G that intersect. If K,U is a closed-open pair in G, we prove…

The lazy algorithm for a real base $\beta$ is generalized to the setting of Cantor bases $\boldsymbol{\beta}=(\beta_n)_{n\in \mathbb{N}}$ introduced recently by Charlier and the author. To do so, let $x_{\boldsymbol{\beta}}$ be the greatest…

Let $S=K[x_1,\dots,x_n]$ be the standard graded polynomial ring, with $K$ a field, and let ${\bf t}=(t_1,\ldots,t_{d-1})\in{\mathbb{Z}}_{\ge 0}^{d-1}$, $d\ge 2$, be a $(d-1)$-tuple whose entries are non negative integers. To a ${\bf…

For a simplicial complex $\Delta$, the affect of the expansion functor on combinatorial properties of $\Delta$ and algebraic properties of its Stanley-Reisner ring has been studied in some previous papers. In this paper, we consider the…

In this paper we describe an algorithm that takes as input a description of a semi-algebraic set $S \subset \R^k$, defined by a Boolean formula with atoms of the form $P > 0, P < 0, P=0$ for $P \in {\mathcal P} \subset \R[X_1,...,X_k],$ and…

We investigate the shadow cast by a regular black hole in scalar-tensor-vector mOdified gravity theory. This black hole differs from a Schwarzschild-Kerr black hole by the dimensionless parameter $\beta$. The size of the shadow depends on…

The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of…

We prove an inequality for the f-vectors of anti-self-polar polytopes conjectured by Katz in 1989. The proof uses Kalai's combinatorial inequality based on a result of Whiteley. The inequality can also be obtained from the results of…

We introduce a generic framework to provide bounds related to the pair correlation of sequences belonging to a wide class. We consider analogues of Montgomery's form factor for zeros of the Riemann zeta function in the case of arbitrary…

We give a combinatorial evaluation of Iwahori Whittaker functions for unramified genuine principal series representations on metaplectic covers of the general linear group over a non-archimedean local field. To describe the combinatorics,…

For any $\ell > 0$, we present an algorithm which takes as input a semi-algebraic set, $S$, defined by $P_1 \leq 0,...,P_s \leq 0$, where each $P_i \in \R[X_1,...,X_k]$ has degree $\leq 2,$ and computes the top $\ell$ Betti numbers of $S$,…

Talenti inequalities are a central feature in the qualitative analysis of PDE constrained optimal control as well as in calculus of variations. The classical parabolic Talenti inequality states that if we consider the parabolic equation…

We study correlation bounds under pairwise independent distributions for functions with no large Fourier coefficients. Functions in which all Fourier coefficients are bounded by $\delta$ are called $\delta$-{\em uniform}. The search for…

A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is…

In previous work, the author has extended the concept of regular and irregular primes to the setting of arbitrary totally real number fields k_{0}, using the values of the zeta function \zeta_{k_{0}} at negative integers as our ``higher…

In this paper we consider the problem of bounding the Betti numbers, $b_i(S)$, of a semi-algebraic set $S \subset \R^k$ defined by polynomial inequalities $P_1 \geq 0,...,P_s \geq 0$, where $P_i \in \R[X_1,...,X_k]$ and $\deg(P_i) \leq 2$,…

Examples of discontinuous functions already appear in the work of Euler, Abel, Dirichlet, Fourier, and Bolzano. A ground-breaking discovery due to Baire was that many discontinuous functions are well-behaved in that they are the pointwise…

Using the Bethe ansatz analysis as was reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly…