Related papers: Barred Preferential Arrangements
A preferential arrangement of a finite set is an ordered partition. Associated with each such ordered partition is a chain of subsets or blocks endowed with a linear order. The chain may be split into sections by the introduction of a…
A barred preferential arrangement is a preferential arrangement onto which a number of identical bars are inserted in between the blocks of the preferential arrangement. In this study we examine combinatorial properties of barred…
When one inserts a number of identical bars in between blocks of an ordered set partition, they get a barred preferential arrangement. In this study we define a new generalization of barred preferential arrangements, by considering barred…
A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by…
Given an ordered set partition, when one insert a number of bars in-between the blocks of the ordered set partition the result is a barred preferential arrangement. In this study, using the notion of barred preferential arrangements we…
A preferential arrangement of a set $X_n=\{1,2,...,n\}$ is an ordered partition of the set $X_n$ induced with a linear order. Separation of blocks of a preferential arrangement with bars result in the notation of barred preferential…
An ordered set-partition (or preferential arrangement) of n labeled elements represents a single ``hierarchy''; these are enumerated by the ordered Bell numbers. In this note we determine the number of ``hierarchical orderings'' or…
A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
Patience Sorting is a combinatorial algorithm that can be viewed as an iterated, non-recursive form of the Schensted Insertion Algorithm. In recent work the authors have shown that Patience Sorting provides an algorithmic description for…
An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non-nesting edges, called queues. The stack (queue)…
We discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives ($A,B,C$) we reduce the $(3!)^3 = 216$ possible…
We characterize the order of principal congruences of a bounded lattice as a bounded ordered set. We also state a number of open problems in this new field.
The nth r-extended Lah-Bell number is defined as the number of ways a set with $n+r$ elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to…
We consider an extension of the setting of label ranking, in which the learner is allowed to make predictions in the form of partial instead of total orders. Predictions of that kind are interpreted as a partial abstention: If the learner…
In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different…
We present a systematic approach for constructing bar frameworks that are rigid but not first-order rigid, using constrained optimization. We show that prestress stable (but not first-order rigid) frameworks arise as the solution to a…
A balanced pair in a finite ordered set $P=(V,\leq)$ is a pair $(x,y)$ of elements of $V$ such that the proportion of linear extensions of $P$ that put $x$ before $y$ is in the real interval $[1/3, 2/3]$. We prove that every finite $N$-free…
In this paper, we consider ordered set partitions obtained by imposing conditions on the size of the lists, and such that the first $r$ elements are in distinct blocks, respectively. We introduce a generalization of the Lah numbers. For…
In this paper we address the characterization of the structure of condensed materials, periodic and non-periodic. Carrying out an extensive study of over 7000 different groundstate structures of a 2D lattice model of binary packing, we find…