Search Results for ""

For a subgroup H of a group G and an element x of G, define xH to be the set {xh:h in H} and Hx to be the set {hx:h in H}. A subset of G of the form xH for some x in G is ...

French curves are plastic (or wooden) templates having an edge composed of several different curves. French curves are used in drafting (or were before computer-aided design) ...

The group theoretical term for what is known to physicists, by way of its connection with matrix traces, as the trace. The powerful group orthogonality theorem gives a number ...

Sarnak's constant is the constant C_(Sarnak) = product_(p>=3)(1-(p+2)/(p^3)) (1) = 0.7236484022... (2) (OEIS A065476), where the product is over the odd primes.

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

The antenna graph is the graph on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["AntennaGraph"].

The cricket graph is the 5-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["CricketGraph"].

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

The dart graph is the 5-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["DartGraph"].

The diamond graph is the simple graph on 4 nodes and 5 edges illustrated above (Brandstädt et al. 1987, p. 18). It is isomorphic to the complete tripartite graph K_(1,1,2) ...