Related papers: Linearly Ordered Families of Baire 1 Functions
Partial orders are a natural model for the social hierarchies that may constrain "queue-like" rank-order data. However, the computational cost of counting the linear extensions of a general partial order on a ground set with more than a few…
We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in…
In this article we discuss the operations of partitions (sequence of disjoint finite subsets) which are quotient, insertion, composition and Lie bracket. Moreover, we discuss applications of those operations for Feymman diagrams and…
Every reduced ring $R$ has a natural partial order defined by $a\le b$ if $a^2=ab$; it generalizes the natural order on a boolean ring. The article examines when $R$ is a lower semi-lattice in this order with examples drawn from weakly Baer…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if…
In the work we discuss the benefit of using bitwise operations in programming. Some interesting examples in this respect have been shown. What is described in detail is an algorithm for sorting an integer array with the substantial use of…
In the present paper we propose a new approach on `distributed systems': the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
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…
Partial orders are used extensively for modeling and analyzing concurrent computations. In this paper, we define two properties of partially ordered sets: width-extensibility and interleaving-consistency, and show that a partial order can…
We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.
We investigate the class of bisymmetric and quasitrivial binary operations on a given set $X$ and provide various characterizations of this class as well as the subclass of bisymmetric, quasitrivial, and order-preserving binary operations.…
We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions…
This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…
We elaborate on the notion of a filtration of an operad defined in terms of a lattice-valued operad serving as an indexing object. That covers ordinary integer-indexed filtrations of associative algebras and operads as a special case, yet…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
We study some natural operators acting on configurations of points and lines in the plane and remark that many interesting configurations are fixed points for these operators. We review ancient and recent results on line or point…