2
$\begingroup$

Consider colorings of n-dimensional complexes. Given a complex $C$, and a coloring of $C$, a simplex $\alpha \in C$ is said (n-x)-complete with respect to this coloring if all its vertices receive at least $(n-x)$ colors.

Sperner's Lemma and the Index lemma relate the number of n-complete simplices in a complex with the number of n-complete simplices in its boundary.

I need to generalize this result to relate the number of $(n-x)$-complete simplices in a complex and their number in its boundary.

Does this generalization already exists ? Any help is welcome.

Thank you.

  • 0
    :) really ! is it so difficult ? Is there any work on this subject, even an incomplete answer to the question ?2012-11-27

0 Answers 0