In an earlier paper, the present authors (2013) [1] introduced the alternating chromatic number for hypergraphs and used Tucker’s Lemma, an equivalent combinatorial version of the Borsuk-Ulam Theorem, to show that the alternating chromatic number is a lower bound for the chromatic number. In this paper, we determine the chromatic number of some families of graphs by specifying their alternating...

We present a theory to investigate electrokinetic behavior, namely, electrorotation and dielectrophoresis under alternating current (ac) applied fields for a pair of touching inhomogeneous colloidal particles and biological cells. These inhomogeneous particles are treated as graded ones with physically motivated model dielectric and conductivity profiles. The mutual polarization interaction bet...

We let A(n) equal the number of n×n alternating sign matrices. From the work of a variety of sources, we know that

We study the convergence of an iterative projection/reflection algorithm originally proposed for solving what are known as phase retrieval problems in optics. There are two features that frustrate any analysis of iterative methods for solving the phase retrieval problem: nonconvexity and infeasibility. The algorithm that we developed, called Relaxed Averaged Alternating Reflections (RAAR), was ...

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...

In this paper, we obtain several new classes of Wilf-equivalent patterns for alternating permutations. In particular, we prove that for any nonempty pattern τ , the patterns 12 . . . k ⊕ τ and k . . . 21 ⊕ τ are Wilf-equivalent for alternating permutations, paralleling a result of Backelin, West, and Xin for Wilf-equivalence for