A 2-coloring of the n-cube in the n-dimensional Euclidean space can be considered as an assignment of weights of 1 or 0 to the vertices. Such a colored ncube is said to be balanced if its center of mass coincides with its geometric center. Let Bn,2k be the number of balanced 2-colorings of the n-cube with 2k vertices having weight 1. Palmer, Read, and Robinson conjectured that for n ≥ 1, the se...

accurate calculation of reliability index is very important for the reliability analysis of structures. in some limit state functions with nonlinear characteristic and several local optimum design points, the computational reliability methods may not appropriately determine the failure probability, and iterative reliability approaches may be converged to local optimum design points. in this pap...

A 321-k-gon-avoiding permutation π avoids 321 and the following four patterns: k(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · (k − 1)(k + 1), k(k + 2)(k + 3) · · · (2k − 1)(2k)12 · · · (k − 1)(k + 1), (k + 1)(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · k, (k + 1)(k + 2)(k + 3) · · · (2k − 1)(2k)123 · · · k. The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW]...

We study sources for torsion in Poincare gauge theory of any dimension, signature, and spin. find that symmetric kinetic terms non-Yang-Mills bosonic fields arbitrary rank drive torsion. Our detailed discussion spin-3/2 Rarita-Schwinger shows they source all independent parts the develop systematic notation spin-(2k+1)/2 spin tensor k n > 2k dimensions. For 0 there is a novel direct coupling be...

Defant, Engen, and Miller defined a refinement of Lassalle's sequence Ak+1 by considering uniquely sorted permutations length 2k+1 whose first element is ℓ. They showed that each such symmetric in ℓ conjectured these sequences are unimodal. We prove the