Observation of Δn=1 dielectronic recombination resonances of boronlike argon

We report here an observation ofn=1 dielectronic recombination resonances of boron-like argon in the energy region 140–195 eV. With the cooler's electron beam as a target, a resolution of approximately 0.6 eV FWHM was obtained in the observed energy range. The energies of the doubly excited states were estimated with a Hartree-Fock calculation, which indicates that the observed resonances are from Ar¹³⁺(1s²2s²2p) to Ar¹²⁺(1s²2s²3l3l) and Ar¹²⁺(1s²2s2p3l3l) transitions.     

Free arrangements and rhombic tilings

Let Z be a centrally symmetric polygon with integer side lengths. We answer the following two questions:

1. When is the associated discriminantal hyperplane arrangementfree in the sense of Saito and Terao?
2. When areall of the tilings of Z by unit rhombicoherent in the sense of Billera and Sturmfels?

Surprisingly, the answers to these two questions are very similar. Furthermore, by means of an old result of MacMahon on plane partitions and some new results of Elnitsky on rhombic tilings, the answer to the first question helps to answer the second. These results then also give rise to some interesting geometric corollaries. Consideration of the discriminantal arrangements for some particular octagons leads to a previously announced counterexample to the conjecture by Saito [ER2] that the complexified complement of a real free arrangement is aK (π, 1) space.