Given a permutation π ∈ S n , construct a graph G π on the vertex set {1, 2, . . . , n} by joining i to j if (i) i < j and π(i) < π( j) and (ii) there is no k such that i < k < j and π(i) < π(k) < π( j). We say that π is forest-like if G π is a forest. We first characterize forestlike permutations in terms of pattern avoidance, and then by a certain linear map being onto. Thanks to recent results of Woo and Yong, these show that forest-like permutations characterize Schubert varieties which are locally factorial. Thus forest-like permutations generalize smooth permutations (corresponding to smooth Schubert varieties).We compute the generating function of forest-like permutations. As in the smooth case, it turns out to be algebraic. We then adapt our method to count permutations for which G π is a tree, or a path, and recover the known generating function of smooth permutations.

Table of Contents SMD solvated (U)M06/def2-TZVPPD//(U)M06/cc-pwCVDZ-PP[aug-cc-pVDZ] xyz coordinates and energies (hartree) …………..

Linear polymeric amines on carbon nanotubes are stable to humidity, require less energy for desorption and adsorb 30 wt% CO2.

The synthesis of a series of Ti complexes of an aryllinked bis-phenoxide ligand, 3,3″-di-tert-butyl-5,5″-dimethyl-[1,1′:2′,1″-terphenyl]-2,2″-bis(olate), (TPO)H 2 , is reported. This ortho-linked terphenyl ligand builds on previously reported metaand para-linked terphenyl-based ligands, completing the isomeric series of terphenoxide ligands. The 4-coordinate (TPO)Ti-(NMe 2 ) 2 is an active catalyst for alkyne hydroamination with a variety of arylamines, revealing good regioselectivity in reactions with unsymmetric alkynes. Terminal alkynes such as phenylacetylene undergo additional insertion reactions with the key azatitanacyclobutene intermediates, providing further evidence that Ti aryloxide complexes are susceptible to this further reactivity.

M06 density functional theory calculations reveal that arene C−H functionalization by the p-block main-groupmetal complex Tl III (TFA) 3 (TFA = trifluoroacetate) occurs by a C−H activation mechanism akin to transition-metal-mediated C− H activation. For benzene, toluene, and xylenes a one-step C−H activation is preferred over electron transfer or proton-coupled electron transfer. The proposed C−H activation mechanism is consistent with calculation and comparison to experiment, of arene thallation rates, regioselectivity, and H/D kinetic isotope effects. For tetramethyl-and pentamethyl-substituted arenes, electron transfer becomes a competitive pathway and thermodynamic and kinetic calculations correctly predict the experimentally reported electron transfer crossover region. These calculations show that p-block metals activate strong hydrocarbon C−H bonds through organometallic intermediates and changes in arene functional groups can result in a shift from C−H activation to electron transfer.