Is every oriented simplicial complex a $\Delta$-complex?

Solution 1:

Instead of ordering the vertices of each simplex separately, just pick a single total ordering on all the vertices of your simplicial complex, and then restrict it to get an ordering of the vertices for each simplex. This will then make every face of each simplex have its vertices in the same order as the original simplex, so that you get a $\Delta$-complex.

$\Delta u=\text{constant}$ in a domain with von Neumann boundary condition

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