We study new statistics on permutations that are variations on the descent and the inversion statistics. In particular, we consider the alternating descent set of a permutation σ = σ1σ2 · · · σn defined as the set of indices i such that either i is odd and σi > σi+1, or i is even and σi < σi+1. We show that this statistic is equidistributed with the odd 3-factor set statistic on permutations σ̃ ...

An alternating permutation of length n is a permutation π = π1π2 · · ·πn such that π1 < π2 > π3 < π4 > · · · . Let An denote the set of alternating permutations of {1, 2, . . . , n}, and let An(σ) be the set of alternating permutations in An that avoid a pattern σ. Recently, Lewis used generating trees to enumerate A2n(1234), A2n(2143) and A2n+1(2143), and he posed some conjectures on the Wilf-...

This paper presents the effects of instrument transformers connection points on the measured impedance by distance relays in the presence of Flexible Alternating Current Transmission System (FACTS) devices with series connected branch. Distance relay tripping characteristic itself depends on the power system structural conditions, pre-fault operational conditions, and especially the ground ...

In this paper we apply answer set programming to solve alternating Boolean equation systems. We develop a novel characterization of solutions for variables in disjunctive and conjunctive Boolean equation systems. Based on this we devise a mapping from Boolean equation systems with alternating fixed points to normal logic programs such that the solution of a given variable of an equation system ...

We prove a conjecture of Cohn and Propp, which refines a conjecture of Bosley and Fidkowski about the symmetry of the set of alternating sign matrices (ASMs). We examine data arising from the representation of an ASM as a collection of paths connecting 2n vertices and show it to be invariant under the dihedral group D2n rearranging those vertices, which is much bigger than the group of symmetri...

Using the correspondence between alternating permutations and pairs of matchings, we present a combinatorial proof for the enumeration of alternating permutations with given peak set. Moreover, we give a refinement according to the number of left to right maxima.

We define a class Ln,k of permutations that generalizes alternating (up-down) permutations. We then give bijective proofs of certain pattern-avoidance results for this class. The bijections employed include are a modified form of the RSK insertion algorithm and a different bijection with RSK-like properties. As a special case of our results, we give two bijections between the set A2n(1234) of a...

a new method was developed for the spectral resolution by further determination of three- and  four-component  mixtures  of  drugs in urine samples through  the complementary application of multivariate curve resolution-alternating least squares with correlation  constraint. in the current study, a simple method was proposed to construct a calibration set for the mixture of drugs in the presenc...

George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege’s inconsistent Axiom V. We build on Boolos’s interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of the principle of limitation of size. After providing a complete structural description of all...