For a d-dimensional cell complex Γ with H̃i(Γ) = 0 for −1 6 i < d, an idimensional tree is a non-empty collection B of i-dimensional cells in Γ such that H̃i(B ∪ Γ(i−1)) = 0 and w(B) := |H̃i−1(B ∪ Γ(i−1))| is finite, where Γ(i) is the iskeleton of Γ. The i-th tree-number is defined ki := ∑ B w(B) 2, where the sum is over all i-dimensional trees. In this paper, we will show that if Γ is acyclic and...

In this paper we study group actions on quasi-median graphs, or 'CAT(0) prism complexes', generalising the notion of CAT(0) cube complexes. We consider hyperplanes in a graph $X$ and define contact $\mathcal{C}X$ for these hyperplanes. show that is always quasi-isometric to tree, result Hagen, under certain conditions action $G \curvearrowright X$ induces an acylindrical \mathcal{C}X$, giving a...

aminocarboxylic acids, such as 2-aminobenzoic acid, react easily with [ir(cod)(pme3)3]cl, (cod=1,5-cyclooctadiene), in thf to produce hydridoaminocarboxylato iridium(iii) complexes in high yields. these octahedral complexes are formed via oxidative addition reaction of the o-h bond of the carboxylic group with the central metal. the starting iridium(i) complex losses the cod molecule, the chlor...

We show that the poset of non-trivial partitions of {1, 2, . . . , n} has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the symmetric groups Σn and Σn+1 on the homology and cohomology of this partially-ordered set. AMS Classification 05E25; 17B60, 55P91

We introduce the Stellar decomposition, a model for efficient topological data structures over broad range of simplicial and cell complexes. A decomposition complex is collection regions indexing complex's vertices cells such that each region has sufficient information to locally reconstruct star its vertices, i.e., incident in region's vertices. decompositions are general they can compactly re...

We consider topological aspects of decision trees on simplicial complexes, concentrating on how to use decision trees as a tool in topological combinatorics. By Robin Forman’s discrete Morse theory, the number of evasive faces of a given dimension i with respect to a decision tree on a simplicial complex is greater than or equal to the ith reduced Betti number (over any field) of the complex. U...