A balanced pair in an ordered set P = (V,6) is a pair (x, y) of elements of V such that the proportion of linear extensions of P that put x before y is in the real interval [1/3, 2/3]. We prove that every finite N -free ordered set which is not totally ordered has a balanced pair.

Let B and R be point sets (of blue and red points, respectively) in the plane, such that P := B ∪R is in general position, and |P | is even. A line l is balanced if it spans one blue and one red point, and on each open halfplane of l, the number of blue points minus the number of red points is the same. We prove that P has at least min{|B|, |R|} balanced lines. This refines a result by Pach and...

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...

The communicative component of the investigator’s professional activities is a dominant one, as it demonstrates employee’s ability to organize work on basis professionally balanced communication with objects interaction. stage obtaining higher education in institutions specific learning environment sensitive period for development main sociogenic structures personality and identity future profe...