The permutation transformation of tensors is introduced and its basic properties are discussed. The invariance under permutation transformations is studied for some important structure tensors such as symmetric tensors, positive definite (positive semidefinite) tensors, Z-tensors, M-tensors, Hankel tensors, P-tensors, B-tensors and H-tensors. Finally, as an application of permutation transforma...

We consider a polynomial – which we term the “slope polynomial” – that encodes information about slopes of lines defined by a point-set in finite affine planes. When the aforementioned point-set is the graph of a permutation, we show that constancy of the polynomial is equivalent to the permutation being linear. This has immediate consequences for the structure of the 3-uniform hypergraph of co...

We use simple iterated one-loop graphs in massless Yukawa theory and QED to pose the following question: what are the symmetries of the residues of a graph under a permutation of places to insert subdivergences. The investigation confirms partial invariance of the residue under such permutations: the highest weight transcendental is invariant under such a permutation. For QED this result is gau...

Feng and Zhu defined the permutation tree structure to achieve a running time of O(n logn) for Hartman and Shamir’s 1.5approximation algorithm for sorting genomes by transpositions. The present work describes the first available implementation of this algorithm using permutation trees. Our analysis of Hartman and Shamir’s algorithm also leads to a modified 1.5-approximation algorithm that achie...

A permutation snark is a cubic graph with no 3-edge-colouring that contains a 2-factor consisting of two induced circuits. In the talk we analyse the basic properties of permutation snarks, focusing on the structure of edge-cuts of size 4 and 5. As an application of our knowledge we provide rich families of cyclically 4edge-connected and 5-edge-connected permutation snarks of order 8n+2 for eac...

We report on our experiences with the implementation of a parallel algorithm to compute the cycle structure of a permutation given as an oracle. As a sub-problem, the cycle structure of a modified permutation given as a table that is partitioned over N hard disks has to be computed. While a minor point during algorithm design and analysis, we spent most time to implement and tune this particula...

In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field Fq. For the first time Möbius and Rédei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of Rédei functions an exact formula for ...

We formalize the Type 1.x Generalized Feistel Structure (GFS) in order to fill the gap between Type 1 and Type 2 GFSs. This is a natural extension of Type 1 and Type 2 GFSs, and covers them as special cases. The diffusion property of GFS is known to vary depending on the permutation used in the round function. When we have two non-linear functions in one round, we propose a permutation that has...