Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic...

For positive integers and , consider a multiset of nonempty subsets such that there is unique partition these into partitions . We study the maximum possible size multiset. focus on regime show When for any this lower bound simplifies to we matching upper optimal up factor also compute exactly when

In many applied areas, such as tomography and crystallography, one is confronted by an unknown subset 5 of a measure space (X, X) such as R" , or an unknown function 0 < (j> < 1 on X , having known moments (integrals) relative to a specified class F of functions f:X—*R. Usually, these F-moments do not fully determine the object S or function . We will say that 5 is a set of uniqueness if no ...

For every natural number n ≥ 2 and every finite sequence L of natural numbers, we consider the set UDn(L) of all uniquely decodable codes over an n-letter alphabet with the sequence L as the sequence of code word lengths, as well as its subsets PRn(L) and FDn(L) consisting of, respectively, the prefix codes and the codes with finite delay. We derive the estimation for the quotient |UDn(L)|/|PRn...