A binary poset code of codimension m (of cardinality 2n−m , where n is the code length) can correct maximum m errors. All possible poset metrics that allow codes of codimension m to be m-, (m − 1)-, or (m − 2)-perfect are described. Some general conditions on a poset which guarantee the nonexistence of perfect poset codes are derived; as examples, we prove the nonexistence of r-perfect poset co...

We study a poset N on the free monoid X∗ on a countable alphabet X. This poset is determined by the fact that its total extensions are precisely the standard term orders on X ∗. We also investigate the poset classifying degree-compatible standard term orders, and the poset classifying sorted term orders. For the latter poset, we give a Galois coconnection with the Young lattice.

S. Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529–563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs. We prove that each poset limit can be represented as a kernel on the unit interval with the standard order, thus answering an open question of Janson. We provide two proofs: real-analytic and combinatorial. The co...

We consider the follow poset merging problem: Let X and Y be two subsets of a partially ordered set S. Given complete information about the ordering within both X and Y , how many comparisons are needed to determine the order on X ∪ Y ? This problem is a natural generalization of the list merging problem. While searching in partially ordered sets and sorting partially ordered sets have been con...

We study the higher Bruhat orders B(n, k) of Manin & Schechtman [MaS] and-characterize them in terms of inversion sets,-identify them with the posets ZY(C n+1 ' r ,n+l) of uniform extensions of the alternating oriented matroids C n ' r for r := n—k (that is, with the extensions of a cyclic hyperplane arrangement by a new oriented pseudoplane),-show that B(n, k) is a lattice for k = 1 and for r ...

An occurrence of a consecutive permutation pattern p in a permutation π is a segment of consecutive letters of π whose values appear in the same order of size as the letters in p. The set of all permutations forms a poset with respect to such pattern containment. We compute the Möbius function of intervals in this poset. For most intervals our results give an immediate answer to the question. I...

The dimension of a poset X is the smallest positive integer t for which there exists an embedding of X in the cartesian product of t chains. R. P. Dilworth proved that the dimension of a distributive lattice v L = 2_ is the width of X. In this paper we derive an analogous result for embedding distributive lattices in the cartesian product of chains of bounded length. We prove that for each k > ...

In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. In this article first of all we describe po-flatness propertie...

‎In this paper some properties of weak regular injectivity for $S$-posets‎, ‎where $S$ is a pomonoid‎, ‎are studied‎. ‎The behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎Also‎, ‎some‎ ‎characterizations of pomonoids over which all $S$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎Further‎, ‎we‎ ‎giv...