For the ordered set [n] of n elements, we consider the class Bn of bases B of tropical Plücker functions on 2[n] such that B can be obtained by a series of mutations (flips) from the basis formed by the intervals in [n]. We show that these bases are representable by special wiring diagrams and by certain arrangements generalizing rhombus tilings on the n-zonogon. Based on the generalized tiling...

In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1, 2, 3}, and giv...

For the ordered set [n] of n elements, we consider the class Bn of bases B of tropical Plücker functions on 2[n] such that B can be obtained by a series of mutations (flips) from the basis formed by the intervals in [n]. We show that these bases are representable by special wiring diagrams and by certain arrangements generalizing rhombus tilings on the n-zonogon. Based on the generalized tiling...

For the ordered set [n] of n elements, we consider the class Bn of bases B of tropical Plücker functions on 2[n] such that B can be obtained by a series of mutations (flips) from the basis formed by the intervals in [n]. We show that these bases are representable by special wiring diagrams and by certain arrangements generalizing rhombus tilings on the n-zonogon. Based on the generalized tiling...

We resolve affirmatively some conjectures of Reiner, Stanton, and White [12] regarding enumeration of various classes of matrices which are invariant under certain cyclic row and column rotations. Our results are phrased in terms of the bicyclic sieving phenomenon introduced by Barcelo, Reiner, and Stanton [1]. The proofs of our results use various tools from symmetric function theory such as t...

In this paper we address an open problem which was stated in [A. Arapostathis et al., SIAM J. Control Optim., 31 (1993), pp. 282–344] in the context of discrete-time controlled Markov chains with a compact action space. It asked whether the associated invariant probability distributions are necessarily tight if all stationary Markov policies are stable, in other words if the corresponding chain...

If a potential person would have a good life if he were to come into existence, can we coherently regard his coming into existence as better for him than his never coming into existence? And can we regard the situation in which he never comes into existence as worse for him? In this paper, we argue that both questions should be answered affirmatively. We also explain where prominent arguments t...

The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-points of the network dynamics. However, the number of binary memories so storable scales linearly in the number of neurons, and it has been a longstanding open problem whether robust expo...

Aligning quality outcomes with cost effectiveness is the cornerstone of the direction of health care in the United States. Implementing and supporting an evidence-based practice (EBP) environment requires resources. Because research is a foundational element of the EBP process, resources allocated for nursing research are essential. As part of operational costs, PhD nurse researchers can affirm...

Lovász conjectured that every connected 4-regular planar graph G admits a realization as a system of circles, i.e., it can be drawn on the plane utilizing a set of circles, such that the vertices of G correspond to the intersection and touching points of the circles and the edges of G are the arc segments among pairs of intersection and touching points of the circles. In this paper, (a) we affi...