We consider the computational complexity of the Market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard.

We review Andr\'e Luiz Barbosa's paper"P != NP Proof,"in which the classes P and NP are generalized and claimed to be proven separate. We highlight inherent ambiguities in Barbosa's definitions, and show that attempts to resolve this ambiguity lead to flaws in the proof of his main result.

Voting and assignment are two of the most fundamental settings in social choice theory. For both settings, random serial dictatorship (RSD) is a well-known rule that satisfies anonymity, ex post efficiency, and strategyproofness. Recently, it was shown that computing the resulting probabilities is #P-complete both in the voting and assignment setting. In this paper, we present efficient paramet...

The title compound, C(9)H(22)NOP, was obtained by slow diffusion of oxygen into a toluene solution of (i)Pr(2)PNH(i)Pr. In the crystal, an inter-molecular N-H⋯O hydrogen bond occurs.