We study a hierarchy of five classes of bijections between the edge sets of two graphs: weak maps, strong maps, cyclic maps, orientable cyclic maps, and chromatic maps. Each of these classes contains the next one and is a natural class of mappings for some family of matroids. For example, f: E(G) --t E(H) is cyclic if every cycle (eulerian subgraph) of G is mapped onto a cycle of H. This class ...

We show that Han’s bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutation π with a cyclic major code (s1, s2, . . . , sn) to a permutation σ with a cyclic inversion code (s1, s2, . . . , sn). We also show that the fixed points of Han’s map can be characterized by the strong fixed points ...

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell–Jones conjecture can be reduced to only those virtually cyclic groups that admit a surjection with finite kernel onto a cyclic group. The second is that the Waldhausen Nil gro...

We present an incremental method for concurrent mapping and localization for mobile robots equipped with 2D laser range finders. The approach uses a fast implementation of scan-matching for mapping, paired with a sample-based probabilistic method for localization. Compact 3D maps are generated using a multi-resolution approach adopted from the computer graphics literature, fed by data from a du...