On maximal instantaneous codes

The possible number of islands on the sea

“…Let us denote the set of elements of C with Lebesgue-measure greater than x by C x . As λ( C x ) = x > 0, (3) implies that C x ∈ A, so x ∈ R. Let cl R be the closure of R and x ∈ cl R \ R. Then either x is a left, but not right limit point of R or x = 0. For every x which is not a right limit point of R there exists a y > x rational number such that (x, y) ∩ R = ∅.…”

“…Földes and Singhi [3] examined "full segments" of vectors, which are just rectangular islands of 1 × n tables in our terminology. According to Theorem 4 of [3], 1 ×n tables A whose entries form the lexicographic length sequence of some binary maximal instantaneous code are characterized by |A| many equations. This makes the maximum of {|A|: A is a 1 ×n table} important in coding theory.…”

Cardinality of height function’s range in case of maximally many rectangular islands — computed by cuts

“…The notion of an island comes from information theory. The characterization of the lexicographical length sequences of binary maximal instantaneous codes in [5] uses the notion of full segments, which are one-dimensional islands. Several generalizations of this notion gave interesting combinatorial problems.…”

Elementary Approaches to the Teaching of the Combinatorial Problem of Rectangular Islands

“…The notion of rectangular islands was introduced by G. Czédli. In fact, a one dimensional preimage of the notion comes from information theory; it appeared first in (Földes and Singhi 2006). Based on the notion of full segments of vectors, that paper gives a necessary and sufficient condition for a code to be prefix-free.…”