Related papers: Barred Preferential Arrangements
We are given a set $A$ of buyers, a set $B$ of houses, and for each buyer a preference list, i.e., an ordering of the houses. A house allocation is an injective mapping $\tau$ from $A$ to $B$, and $\tau$ is strictly better than another…
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…
An $L$-matrix is a matrix whose off-diagonal entries belong to a set $L$, and whose diagonal is zero. Let $N(r,L)$ be the maximum size of a square $L$-matrix of rank at most $r$. Many applications of linear algebra in extremal combinatorics…
Sequential allocation is a simple and attractive mechanism for the allocation of indivisible goods. Agents take turns, according to a policy, to pick items. Sequential allocation is guaranteed to return an allocation which is efficient but…
An $\alpha$-greedy balanced pair in an ordered set $P=(V,\leq)$ is a pair $(x,y)$ of elements of $V$ such that the proportion of greedy linear extensions of $P$ that put $x$ before $y$ among all greedy linear extensions is in the real…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
We consider linear orders of finite alternatives constructed by aggregating individual preferences. Specifically, we focus on linear orders that respect modified collective preference relations derived from supermajority rules, where…
Various models have been recently proposed to reflect and predict different properties of complex networks. However, the community structure, which is one of the most important properties, is not well studied and modeled. In this paper, we…
We prove that the property of being closed (resp., palindromic, rich, privileged trapezoidal, balanced) is expressible in first-order logic for automatic (and some related) sequences. It therefore follows that the characteristic function of…
We give an overview of combinatoric properties of the number of ordered $k$-factorizations $f_k(n,l)$ of an integer, where every factor is greater or equal to $l$. We show that for a large number $k$ of factors, the value of the cumulative…
We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous…
Much work on argument systems has focussed on preferred extensions which define the maximal collectively defensible subsets. Identification and enumeration of these subsets is (under the usual assumptions) computationally demanding. We…
In this paper, we describe how to get Janet decomposition for a finite set of terms and detect completeness of that set by means of the associated Bar Code. Moreover, we explain an algorithm to find a variable ordering (if it exists) s.t. a…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
A split preorder is a preordering relation on the disjoint union of two sets, which function as source and target when one composes split preorders. The paper presents by generators and equations the category SplPre, whose arrows are the…
We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a…
We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
This article provides a link diagram to visualize relations between two ordered sets representing precedences on decision-making options or solutions to strategic form games. The diagram consists of floating loops whose any two loops cross…
A (v,b,r,k) combinatorial configuration is a (r,k)-biregular bipartite graph with v vertices on the left and b vertices on the right and with no cycle of length 4. Combinatorial configurations have become very important for some…