A range of research has explored the problem of generating referring expressions that uniquely identify a single entity from the shared context. But what about expressions that identify sets of entities? In this paper, I adapt a state-of-the-art semantics for plural descriptions—using covers to abstract collective and distributive readings and using sets of assignments to represent dependencies...

A bidirectional transformation on a pair of sets of models induces two principal equivalence relations on each set of models. Since a model can be uniquely identified by specifying its equivalence class in each of these relations, they function as a coordinate system for the model sets, with respect to the transformation. We prove some results relating to this observation. Using them we give th...

Let S be a set of functions with common domain D. We say X, a subset of D, an interpolation set for S if the values on X uniquely determine a function f in S. Recently, Piotr Indyk gave an explicit construction of interpolation sets of size O(k log n) for the family of boolean functions on n variables which depend symmetrically on at most k variables. Using perfect hash families, we have a vari...

We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements of the considered ordered sets might carry some additional information. In this way an analytic proof of generalized Cauchy identities from the previous work...

It has been shown that univalent circle packings lling in the complex plane C are unique up to similarities of C. Here we prove that bounded degree branched circle packings properly covering C are uniquely determined, up to similarities of C, by their branch sets. In particular, when branch sets of the packings considered are empty we obtain the earlier result. We also establish a circle packin...

the aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $s_{h}$ and  $t_{h},$ respectively. it is shown that $t_{h}=s_{h}$ if and only if $beta=beta^{*}.$ we also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

It has been shown that univalent circle packings filling in the complex plane C are unique up to similarities of C. Here we prove that bounded degree branched circle packings properly covering C are uniquely determined, up to similarities of C, by their branch sets. In particular, when branch sets of the packings considered are empty we obtain the earlier result. We also establish a circle pack...

Let X be a cofunctor from O to sets. Let Xn = X({0, 1, · · · , n}). The face function dj : Xn → Xn−1 is induced by the inclusion d : {0, · · · , n − 1} → {0, · · ·n} with d(i) = i for i < j, d(i) = i + 1 for i ≥ j for 0 ≤ j ≤ n. The degeneracy function sj : Xn → Xn+1 is induced by s : {0, · · · , n+ 1} → {0, · · · , n} with s(i) = i for i ≤ j and s(i) = i− 1 for i > j for 0 ≤ j ≤ n. The simplic...

The reconstruction of 8-connected but not 4-connectedhv-convex discrete sets from few projections is considered. An algorithm is given with worst case complexity of O(mnmin{m, n}) to reconstruct all sets with given horizontal and vertical projections. Experimental results are also presented. It is shown, that using also the diagonal projections the algorithm can be speeded up having complexity ...

Properties of homogeneous segment sets are investigated in this paper. A universal characterization of homogeneous sets is presented in the form of a polynomial algorithm which decides whether or not a set S is homogeneous with respect to S∗. It is shown that any set of homogeneous segments can be reduced to the uniquely determined minimal base and a polynomial algorithm solving this task is pr...