Isometry Classes of Indecomposable Linear Codes

In the constructive theory of linear codes, we can restrict attention to the isometry classes of indecomposable codes, as it was shown by Slepian

On permutation characters of wreath products

AbstractIt is known that the character rings of symmetric groups Sn and the character rings of hyperoctahedral groups S2≀Sn are generated by (transitive) permutation characters. These results of Young are generalized to wreath products G≀H (G a finite group, H a permutation group acting on a finite set). It is shown that the character ring of G≀H is generated by permutation characters if this holds for G, H and certain subgroups of H. This result can be sharpened for wreath products G≀Sn;if the character ring of G has a basis of transitive permutation characters, then the same holds for the character ring of G≀Sn

CASE via MS: Ranking Structure Candidates by Mass Spectra

Two important tasks in computer-aided structure elucidation (CASE) are the generation of candidate structures from a given molecular formula, and the ranking of structure candidates according to compatibility with an experimental spectrum. Candidate ranking with respect to electron impact mass spectra is based on virtual fragmentation of a candidate structure and comparison of the fragments’ isotope distributions against the spectrum of the unknown compound, whence a structure–spectrum compatibility matchvalue is computed. Of special interest is the matchvalue’s ability to distinguish between the correct and false constitutional isomers. Therefore a quality score was computed in the following way: For a (randomly selected) spectrum–structure pair from the NIST MS library all constitutional isomers are generated using the structure generator MOLGEN. For each isomer the matchvalue with respect to the library spectrum is calculated, and isomers are ranked according to their matchvalues. The quality of the ranking can be quantified in terms of the correct structure’s relative ranking position (RRP). This procedure was repeated for 100 randomly selected spectrum–structure pairs belonging to small organic compounds. In this first approach the RRP of the correct isomer was 0.27 on average

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060