Blancmange Curve - Relation To Simplicial Complexes

Relation To Simplicial Complexes

Let

 N=\binom{n_t}{t}+\binom{n_{t-1}}{t-1}+\ldots+\binom{n_j}{j},\quad
n_t > n_{t-1} > \ldots > n_j \geq j\geq 1.

Define the Kruskal–Katona function


\kappa_t(N)={n_t \choose t+1} + {n_{t-1} \choose t} + \dots + {n_j \choose j+1}.

The Kruskal–Katona theorem states that this is the minimum number of (t − 1)-simplexes that are faces of a set of N t-simplexes.

As t and N approach infinity, (suitably normalized) approaches the blancmange curve.

Read more about this topic:  Blancmange Curve

Famous quotes containing the words relation to and/or relation:

    The proper study of mankind is man in his relation to his deity.
    —D.H. (David Herbert)

    The psychoanalysis of individual human beings, however, teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father.
    Sigmund Freud (1856–1939)