A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say b2, each having repeated elements. We prove some necessary conditions on b2 and show the existence of some particular BPTDs. We also give constructions of infinite families of BPTDs with b1 = 0, including families of ternary t-designs with t ≥ 3.

An-balanced pair in a partially ordered set P = (X; <) is a pair (x; y) of elements of X such that the proportion of linear extensions of P with x below y lies between and 1 ?. The 1=3 ? 2=3 Conjecture states that, in every nite partial order P , not a chain, there is a 1 3-balanced pair. This was rst conjectured in a 1968 paper of Kislitsyn, and remains unsolved. We survey progress towards a r...

Balanced growth has at least two different meanings in economics. In macroeconomics, balanced growth occurs when output and the capital stock grow at the same rate. This growth path can rationalize the long-run stability of real interest rates, but its existence requires strong assumptions. In development economics, balanced growth refers to the simultaneous, coordinated expansion of several se...

Ideally psychologists strive to act ethically within their professional roles. However, they are unlikely to achieve the highest standards of ethical behavior if they become overly legalistic or if they engage in behaviors that can be virtuous in a personal context but harmful in a professional relationship. Such problems may arise when some justify their less-than-optimal behavior based upon a...

We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly (d + 1)-colored) triangulation of a combinatorial d-manifold into another balanced triangulation. These moves form a natural analog of bistellar flips (also known as Pachner moves). Specifically, we establish the following theorem: any two balanced triangulations of a closed combinatorial d-manifold can ...