Adalbert Kerber

Bio: Adalbert Kerber is an academic researcher from University of Bayreuth. The author has contributed to research in topics: Symmetric group & Mathematical chemistry. The author has an hindex of 10, co-authored 15 publications receiving 3060 citations.

The representation theory of the symmetric group

Abstract: 1. Symmetric groups and their young subgroups 2. Ordinary irreducible representations and characters of symmetric and alternating groups 3. Ordinary irreducible matrix representations of symmetric groups 4. Representations of wreath products 5. Applications to combinatories and representation theory 6. Modular representations 7. Representation theory of Sn over an arbitrary field 8. Representations of general linear groups Appendices Index.

Representations of permutation groups

Abstract: Characters of wreath products.- An application to representation theory: Symmetrization of inner tensor products of representations.- An application to combinatorics: The theory of enumeration under group action.

Applied finite group actions

Abstract: 0. Labeled Structures.- 1. Unlabeled Structures.- 2. Enumeration of Unlabeled Structures.- 3. Enumeration by Weight.- 4. Enumeration by Stabilizer Class.- 5. Poset and Semigroup Actions.- 6. Representations.- 7. Further Applications.- 8. Permutations.- 9. Construction and Generation.- 10. Tables.- 11. Appendix.- 12. Comments and References.- References.

From mass to structure: an aromaticity index for high‐resolution mass data of natural organic matter

Abstract: Recent progress in Fourier transform ion cyclotron resonance mass spectrometry (FTICRMS) provided extensive molecular mass data for complex natural organic matter (NOM). Structural information can be deduced solely from the molecular masses for ions with extreme molecular element ratios, in particular low H/C ratios, which are abundant in thermally altered NOM (e.g. black carbon). In this communication we propose a general aromaticity index (AI) and two threshold values as unequivocal criteria for the existence of either aromatic (AI > 0.5) or condensed aromatic structures (AI >= 0.67) in NOM. AI can be calculated from molecular formulae which are derived from exact molecular masses of naturally occurring compounds containing C, H, O, N, S and P and is especially applicable for substances with aromatic cores and few alkylations. In order to test the validity of our model index, AI is applied to FTICRMS data of a NOM deep-water sample from the Weddell Sea (Antarctica), a fulvic acid standard and an artificial dataset of all theoretically possible molecular formulae. For graphical evaluation a ternary plot is suggested for four-dimensional data representation. The proposed aromaticity index is a step towards structural identification of NOM and the molecular identification of black carbon in the environment.

970 million druglike small molecules for virtual screening in the chemical universe database GDB-13.

Abstract: GDB-13 enumerates small organic molecules containing up to 13 atoms of C, N, O, S, and Cl following simple chemical stability and synthetic feasibility rules. With 977 468 314 structures, GDB-13 is the largest publicly available small organic molecule database to date.