We present examples of flag homology spheres whose γvectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In another direction, we show that if a flag (d− 1)-sphere has at most 2d + 2 vertices its γ-vector satisfies the Kruska...

BERNARDO M. ÁBREGO, SILVIA FERNÁNDEZ-MERCHANT, AND BERNARDO LLANO Abstract. Given integers k ≥ 1 and n ≥ 0, there is a unique way of writing n as n = ¡nk k ¢ + ¡ nk−1 k−1 ¢ + ... + ¡ n1 1 ¢ so that 0 ≤ n1 < · · · < nk−1 < nk. Using this representation, the KruskalMacaulay function of n is defined as mk (n) = ¡ nk−1 k−1 ¢ + ¡ nk−1−1 k−2 ¢ + ... + ¡ n1−1 0 ¢ . We show that if a ≥ 0 and a < mk+1 (...

We show how to determine if a given vector can be the signature of a system on a finite number of components and, if so, exhibit such a system in terms of its structure function. The method employs combinatorial results from the theory of (finite) simplicial complexes, and provides a full characterization of signature vectors using a theorem of Kruskal and Katona. We also show how the same appr...

OBJECTIVE To investigate the relationship between oxidative stress and biochemical parameters and the expression of TXNIP, IL-6, IL-1β and TNF-α in peripheral mononuclear cells (PMCs) from type-2 diabetic patients. METHODS We studied 60 males: 20 normal-weight type- 2 diabetic patients (NW), 20 obese diabetic patients (OB) and 20 controls (C). Biochemical and oxidative stress parameters were ...

We give a short new proof of a version of the Kruskal-Katona theorem due to Lovász. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a question of Mubayi. This in turn leads to another combinatorial proof of a stability theorem for intersecting families, which was originally obtained by Fried...

The energy content of electrostatic perturbations about homogeneous equilibria is discussed. The calculation leading to the well-known dielectric (or as it is sometimes called, the wave) energy is revisited and interpreted in light of Vlasov theory. It is argued that this quantity is deficient because resonant particles are not correctly handled. A linear integral transform is presented that so...

We investigate the massless scalar field perturbations of a new loop quantum gravity motivated regular black hole proposed by Ashtekar {\it et al.} in [Phys.Rev.Lett. 121, 241301 (2018), Phys.Rev.D 98, 126003 (2018)]. The spacetime this is distinguished its asymptotic properties: Schwarzschild coordinates one metric functions diverges as $r\to \infty$ even though asymptotically flat. show that ...

We perform the shadow calculation of loop quantum gravity motivated regular black hole recently proposed by Ashtekar, Olmedo and Singh (will be termed AOS hereafter). In process, we also construct rotating inspired solution originally static spherically symmetric applying modified Newman-Janis algorithm. study effects on shadows both non-rotating solutions. It is observed that general shape for...