Jun 2, 2017 · A rack on [n] [ n ] can be thought of as a set of maps (fx)x∈[n] ( f x ) x ∈ [ n ] , where each fx f x is a permutation of [n] [ n ] such that f ...

Jul 24, 2016 · The proof involves considering racks as loopless, edge-coloured directed multigraphs on [n], where we have an edge of colour y between x and z ...

Counting racks of order n ...

If X X X is finite, we call | X | X |X| the order of the rack. Note that conditions 1 and 2 above are equivalent to the statement that for each y y y ...

A sequence of new knot invariants is constructed by using the relationship between the theory of distributive groupoids and knot theory.Bibliography: 3 titles.

Jun 2, 2017 · A rack on [n] can be thought of as a set of maps (f x )x∈ [n] , where each f x is a permutation of [n] such that f (x) f y =f −1 y f x f y ...

A rack on $[n]$ can be thought of as a set of maps $(f_x)_{x \in [n]}$, where each $f_x$ is a permutation of $[n]$ such that $f_{(x)f_y} ...

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting in- variant for classical and virtual ...

This book offers teachers the theoretical basis and practical knowledge to employ the number rack, or rekenrek, as a powerful mathematical tool. Building on the ...

We introduce a modified rack algebra Z[X] for racks X with finite rack rank. N. We use representations of Z[X] into rings, known as rack modules, to define.