Promotion and cyclic sieving via webs

We show that Schützenberger’s promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this action admits the cyclic sieving phenomenon.     

On the Hamming distance in combinatorial optimization problems on hypergraph matchings

In this note we consider the properties of the Hamming distance in combinatorial optimization problems on hypergraph matchings, also known as multidimensional assignment problems. It is shown that the Hamming distance between feasible solutions of hypergraph matching problems can be computed as an optimal value of linear assignment problem. For random hypergraph matching problems, an upper bound on the expected Hamming distance to the optimal solution is derived, and an exact expression is obtained in the special case of multidimensional assignment problems with 2 elements in each dimension.     

Cadmium(II) chloride,bromide and iodide complexes with 4,4′‐bipyridazine: when are diazine and halide bridges (in)compatible?

In poly[di‐μ‐chlorido‐μ‐(4,4′‐bipyridazine)‐κ²N¹:N^1′‐cadmium(II)], [CdCl₂(C₈H₆N₄)]_n, (I), and its isomorphous bromide analogue, [CdBr₂(C₈H₆N₄)]_n, (II), the halide atom lies on a mirror plane and the Cd^II ion resides at the intersection of two perpendicular mirror planes with m2m site symmetry. The pyridazine rings of the ligand lie in a mirror plane and are related to each other by a second mirror plane perpendicular to the first. The compounds adopt the characteristic structure of the [M^IIX₂(bipy)] type (bipy is bipyridine) based on crosslinking of [Cd(μ‐X)₂]_n chains [Cd—Cl = 2.5955 (9) and 2.6688 (9) Å; Cd—Br = 2.7089 (4) and 2.8041 (3) Å] by bitopic rod‐like organic ligands [Cd—N = 2.368 (3)–2.380 (3) Å]. This feature is discussed in terms of supramolecular stabilization, implying that the periodicity of the inorganic chain [Cd...Cd = 3.7802 (4) Å in (I) and 3.9432 (3) Å in (II)] is favourable for extensive parallel π–π stacking of monodentate pyridazine rings, with centroid–centroid distances of 3.7751 (4) Å in (I) and 3.9359 (4) Å in (II). This is not the case for the longer iodide bridges, which cannot stabilize such a pattern. In poly[tetra‐μ‐iodido‐μ₄‐(4,4′‐bipyridazine)‐κ⁴N¹:N²:N^1′:N^2′‐dicadmium(II)], [Cd₂I₄(C₈H₆N₄)]_n, (III), the ligands are situated across a centre of inversion; they are tetradentate [Cd—N = 2.488 (2) and 2.516 (2) Å] and link successive [Cd(μ‐I)₂]_n chains [Cd—I = 2.8816 (3)–3.0069 (4) Å] into corrugated layers.     

Dithiolopyranthione Synthesis,Spectroscopy, and an Unusual Reactivity with DDQ

The bicyclic pyran thiolone tetrahydro‐3αH‐[1,3]dithiolo[4,5‐β]pyran‐2‐thione ( 3a ) engages in a highly unusual fragmentation in the presence of DDQ. The pyran thiolone, 3a , was synthesized by chlorination of 3,4‐dihydro‐2H‐pyran ( 1 ) followed by condensing with CS₂ and NaSH. Reaction of 3a with DDQ generates the isomerized pyran thiolone tetrahydro‐3αH‐[1,3]dithiolo[4,5‐β]pyran‐2‐thione ( 3b ) and 4‐benzyl‐5‐(3‐hydroxypropyl)‐1,3‐dithiole‐2‐thione ( 4 ) via a deep‐seated rearrangement. The identity of 3b was confirmed by single crystal X‐ray analysis: P2₁/c, a = 5.807(9) Å, b = 12.99(2) Å, c = 11.445(15), β = 113.23(6)°. Mechanistic experiments and computational insight is used to explain the likely sequence of events in the highly unusual formation of 4 . Collectively, these results establish fundamental reactivity patterns for further research in this area.     

On optimality of a polynomial algorithm for random linear multidimensional assignment problem

We demonstrate that the linear multidimensional assignment problem with iid random costs is polynomially e{\varepsilon} -approximable almost surely (a.s.) via a simple greedy heuristic, for a broad range of probability distributions of the assignment costs. Specifically, conditions on discrete and continuous distributions of the cost coefficients, including distributions with unbounded support, have been established that guarantee convergence to unity in the a.s. sense of the cost ratio between the greedy solution and optimal solution. The corresponding convergence rates have been determined.     

On Valid Inequalities for Mixed Integer p-Order Cone Programming

We discuss two families of valid inequalities for linear mixed integer programming problems with cone constraints of arbitrary order, which arise in the context of stochastic optimization with downside risk measures. In particular, we extend the results of Atamtürk and Narayanan (Math. Program., 122:1–20, 2010, Math. Program., 126:351–363, 2011), who developed mixed integer rounding cuts and lifted cuts for mixed integer programming problems with second-order cone constraints. Numerical experiments conducted on randomly generated problems and portfolio optimization problems with historical data demonstrate the effectiveness of the proposed methods.     

Asymptotic behavior of the expected optimal value of the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) is a higher-dimensional version of the Linear Assignment Problem that arises in the areas of data association, target tracking, resource allocation, etc. This paper elucidates the question of asymptotical behavior of the expected optimal value of the large-scale MAP whose assignment costs are independent identically distributed random variables with a prescribed probability distribution. We demonstrate that for a broad class of continuous distributions the limiting value of the expected optimal cost of the MAP is determined by the location of the left endpoint of the support set of the distribution, and construct asymptotical bounds for the expected optimal cost.     

A Spherically Shielded Triphenylamine and Its Persistent Radical Cation

This work reports the design and synthesis of a sterically protected triphenylamine scaffold which undergoes one-electron oxidation to form an amine-centered radical cation of remarkable stability. Several structural adjustments were made to tame the inherent reactivity of the radical cation. First, the parent propeller-shaped triphenylamine was planarized with sterically demanding bridging units and, second, protecting groups were deployed to block the reactive positions. The efficiently shielded triphenylamine core can be reversibly oxidized at moderate potentials (+0.38 V, vs. Fc/Fc⁺ in CH₂Cl₂). Spectroelectrochemistry and chemical oxidation studies were employed to monitor the evolution of characteristic photophysical features. To obtain a better understanding of the impact of one-electron oxidation on structural and electronic properties, joint experimental and computational studies were conducted, including X-ray structural analysis, electron paramagnetic resonance (EPR), and density functional theory (DFT) calculations. The sterically shielded radical cation combines various desirable attributes: A characteristic and unobstructed absorption in the visible region, high stability which enables storage for weeks without spectroscopically traceable degradation, and a reliable oxidation/re-reduction process due to effective screening of the planarized triphenylamine core from its environment.     

The Impact of Aggregation on the Photophysics of Spiro‐Bridged Heterotriangulenes

We report on the impact of the central heteroatom on structural, electronic, and spectroscopic properties of a series of spirofluorene‐bridged heterotriangulenes and provide a detailed study on their aggregates. The in‐depth analysis of their molecular structure by NMR spectroscopy and X‐ray crystallography was further complemented by density functional theory calculations. With the aid of extensive photophysical analysis the complex fluorescence spectra were deconvoluted showing contributions from the peripheral fluorenes and the heteroaromatic cores. Beyond the molecular scale, we examined the aggregation behavior of these heterotriangulenes in THF/H₂O mixtures and analyzed the aggregates by static and dynamic light scattering. The excited‐state interactions within the aggregates were found to be similar to those found in the solid state. A plethora of morphologies and superstructures were observed by scanning electron microscopy of drop‐casted dispersions.