We introduce a statistic pmaj(P ) for partitions of [n], and show that it is equidistributed with cr2, the number of 2-crossings, over all partitions of [n] with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inv and maj. © 2007 Elsevier Inc. All rights reserved.

We characterize supersolvable lattices in terms of a certain modular type relation. McNamara and Thomas earlier characterized this class as those graded having maximal chain that consists left-modular elements. Our characterization replaces the condition gradedness with second modularity on

Objective: In this study, we aimed to validate the accuracy of computed tomography-based attenuation correction (CTAC) using the bilinear scaling method.Methods: The measured attenuation coefficient (μm) was compared to a theoretical attenuation coefficient (μt ) using four different CT scanners and an RMI 467 phantom. The effective energy of the CT beam X-rays was calculated, using the aluminu...

biharmonic surfaces in euclidean space $mathbb{e}^3$ are firstly studied from a differential geometric point of view by bang-yen chen, who showed that the only biharmonic surfaces are minimal ones. a surface $x : m^2rightarrowmathbb{e}^{3}$ is called biharmonic if $delta^2x=0$, where $delta$ is the laplace operator of $m^2$. we study the $l_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

The following equivalent results in the Boolean lattice 2 are proven. (a) Every fibre of 2 contains a maximal chain. (b) Every cutset of 2 contains a maximal antichain. (c) Every red-blue colouring of the vertices of 2 produces either a red maximal chain or a blue maximal antichain. (d) Given any n antichains in 2 there is a disjoint maximal antichain. Statement (a) is then improved to: (a') Ev...

It is shown that the behavior of an m-port circuit maximal monotone elements can be expressed as a zero sum operator containing elements, and structured skew-symmetric linear representing interconnection structure, together with output transformation. The Condat–Vũ algorithm solves inclusion problems this form, may used to solve for periodic steady-state behavior, given excitation at each port,...