it is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

The band structure for a crystal generally consists of connected components in energy-momentum space, known as complexes. Here, we explore fundamental aspect regarding the maximal number bands that can be accommodated single complex. We show that, principle, complex have no finite upper bound certain space groups. This means infinitely many entangle together, forming pattern stable against symm...