The result, due to Henckell, Margolis, Pin and Rhodes modulo Ash’s solution to the pointlike conjecture, that every finite block group divides a power group, has long been considered to be one of the deepest results in finite semigroup theory. However, the proof is not constructive. Solving a long-standing problem, we provide in this paper an explicit construction of such a division. We also ge...

We consider the problem of selecting fair divisions a heterogeneous divisible good among set agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations under fairness notion envy-freeness. Maxsum allocations can also be found alternative notions such as equitability. In this paper, we examine properties these allocat...