Related papers: Partial-conjugates and Dimensionality of Posets
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…
We consider the concept of rank as a measure of the vertical levels and positions of elements of partially ordered sets (posets). We are motivated by the need for algorithmic measures on large, real-world hierarchically-structured data…
In order theory, a rank function measures the vertical "level" of a poset element. It is an integer-valued function on a poset which increments with the covering relation, and is only available on a graded poset. Defining a vertical measure…
Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This…
The {\it profile} of a relational structure $R$ is the function $\phi_R$ which counts for every integer $n$ the number of its $n$-element substructures up to an isomorphism. Many counting functions are profiles. Interesting examples come…
Combinatorial preference aggregation has many applications in AI. Given the exponential nature of these preferences, compact representations are needed and ($m$)CP-nets are among the most studied ones. Sequential and global voting are two…
A recently introduced restricted variant of the multidimensional stable roommate problem is the roommate diversity problem: each agent belongs to one of two types (e.g., red and blue), and the agents' preferences over the coalitions solely…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of…
Conditional preference networks (CP-nets) are a graphical representation of a person's (conditional) preferences over a set of discrete variables. In this paper, we introduce a novel method of quantifying preference for any given outcome…
The quality of consequences in a decision making problem under (severe) uncertainty must often be compared among different targets (goals, objectives) simultaneously. In addition, the evaluations of a consequence's performance under the…
We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized…
We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified…
We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the…
Analyzing the consistency of preferences is an important step in decision making with pairwise comparison matrices, and several indices have been proposed in order to estimate it. In this paper we prove the proportionality between some…
Linearizing two partial orders to maximize the number of adjacencies and minimize the number of breakpoints is APX-hard. This holds even if one of the two partial orders is already a linear order and the other is an interval order, or if…
A preferential arrangement of a set is a total ordering of the elements of that set with ties allowed. A barred preferential arrangement is one in which the tied blocks of elements are ordered not only amongst themselves but also with…
In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these…
We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting that have constant failure rate. In spite of the minimal algebraic structure, there is a…