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Let Π = B1/B2/ ··· /Bk be any set partition of [n] = {1, 2,..., n} satisfying that entries are increasing in each block and blocks are arranged in increasing order of their first entries. Then Callan defined the flattened Π to be the permutation of [n] obtained by erasing the divers between its blocks, and Callan also enumerated the number of set partitions of [n] whose flattening avoids a single 3-letter pattern. Mansour posed the question of counting set partitions of [n] whose flattening avoids a pattern of length 4. In this paper, we present the number of set partitions of [n] whose flattening avoids one of the patterns: 1234, 1243, 1324, 1342, 1423, 1432, 3142 and 4132.

A novel series of mGluR2 positive allosteric modulators (PAMs), 1-[(1-methyl-1H-imidazol-2-yl)methyl]-4-phenylpiperidines, is herein disclosed. Structure-activity relationship studies led to potent, selective mGluR2 PAMs with excellent pharmacokinetic profiles. A representative lead compound (+)-17e demonstrated dose-dependent inhibition of methamphetamine-induced hyperactivity and mescaline-induced scratching in mice, providing support for potential efficacy in treating psychosis.

The synthesis and structure–activity relationship (SAR) of a novel series of 3-(imidazolyl methyl)-3-aza-bicyclo[3.1.0]hexan-6-yl)methyl ethers, derived from a high throughput screening (HTS), are described. Subsequent optimization led to identification of potent, metabolically stable and orally available mGluR2 positive allosteric modulators (PAMs).