In this paper we study the resolution of a facet ideal associated with a special class of simplicial complexes introduced by Faridi. These simplicial complexes are called trees, and are a generalization (to higher dimensions) of the concept of a tree in graph theory. We show that the Koszul homology of the facet ideal I of a tree is generated by the homology classes of monomial cycles, determin...

We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms of the eigenvalues of its cellular Laplacian operators, generalizing a previous result for simplicial complexes. As an application, we obtain explicit formulas for spanning tree enumerators and Laplacian eigenvalues of cubes; the latter are integers. We prove a weighted version of the eigenvalue formula, pr...

lanthanide(iii) chloro complexes of 4[n-(4’-hydroxy-3’-methoxybenzalidene) amino] antipyrine semicarbazone (hmbaaps) (i) and 4[n-(3’,4’,5’-trimethoxybenzalidene) amino] antipyrine semicarbazone (tmbaaps) (ii) with the general composition lncl3.2l (ln = la, pr, nd, sm, gd, tb, dy or ho; l = hmbaaps or tmbaaps) are reported. all the complexes were synthesized in ethanolic medium and refluxed the ...

environmental pollution with heavy metals is a global struggle. phytoremediation is an effectiveand low-cost technology for refinement of polluted soils. this research was conducted in zanjan province(located in north west iran) where metallurgical industries are developed quickly. in this study, based on theheavy metals contamination of soil in the studied area six sampling sites were selected...

Protein side-chain packing is a critical component in obtaining the 3D coordinates of a structure and drug discovery. Single-domain protein side-chain packing has been thoroughly studied. For instance, our efficient tree decomposition algorithm TreePack has been re-implemented in SCWRL, the widely-used side-chain packing program, for monomer side-chain packing. A major challenge in generalizing...

Abstract In this paper we study natural reconfiguration spaces associated to the problem of distributing a fixed number resources labeled nodes tree network, so that no node is left empty. These turn out be cubical complexes, which can thought as higher-dimensional geometric extensions combinatorial Stirling partitioning set named objects into non-empty parts. As our main result, prove these co...

We investigate the virtual specialness of a compact cube complex X that splits as graph nonpositively curved complexes. prove when each vertex space has word-hyperbolic $$\pi _1$$ and _1X$$ “finite stature” relative to its edge groups. The results generalize motivating case tree $$\times $$ lattices are products.