Bibliography of publications by Rudolf Ahlswede
Information Theory, Combinatorics, and Search Theory
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We discovered a new and simple shifting technique. It makes it possible to prove results on shadows like the Kruskal-Katona theorem without any additional arguments.As another application we obtain the following new result. For s, d, k ∈ N, 1 ≤ d ≤ s, d ≤ k define the subclass of (N k) (the k-subsets of N) B(k, s, d) = {B ∈ (N k) : |B ∩ [1,s]| ≥ d}. Let A ⊂ B(k, s, d) and |A| = m. Then the cardinality of the l-shadow of A is minimal if A consists of the first m elements of B(k, s, d) in colexicographic order. A more general form of this result is given as well. Other applications are to be expected.