The problem of determining the maximum size La(n, P ) that a P -free subposet of the Boolean lattice Bn can have, attracted the attention of many researchers, but little is known about the induced version of these problems. In this paper we determine the asymptotic behavior of La∗(n, P ), the maximum size that an induced P -free subposet of the Boolean lattice Bn can have for the case when P is...

We show that the order complex of poset nonempty intervals, ordered by inclusion, is a Tchebyshev triangulation original poset. Besides studying properties this transformation, we dual type B permutohedron combinatorially equivalent to suspension intervals Boolean algebra (with minimum and maximum elements removed).

To investigate pathways to adjust the charge carrier concentration and optimize thermoelectric properties, we characterized structural thermal stability, performance of pristine Cl-doped Cu5+εSn2−εS7. We demonstrate that Cl doping in Cu5Sn2S7-type monoclinic compounds induces a collapse long-range cationic ordering, ultimately leading sphalerite-type cubic phase by ordered [Sn(S,Cl)4]x clusters...

(2) Let L, S, T be complete non empty posets, f be a CLHomomorphism of L, S, and g be a CLHomomorphism of S, T . Then g · f is a CLHomomorphism of L, T . (3) For every non empty relational structure L holds idL is infs-preserving. (4) For every non empty relational structure L holds idL is directed-sups-preserving. (5) For every complete non empty poset L holds idL is a CLHomomorphism of L, L. ...

Let V be an n-dimensional vector space over a finite field Fq and P = {1, 2, . . . , n} a poset. We consider on V the poset-metric dP . In this paper, we give a complete description of groups of linear isometries of the metric space (V, dP ), for any poset-metric dP . We show that a linear isometry induces an automorphism of order in poset P , and consequently we show the existence of a pair of...

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W -orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A ...

Let G be a simple, undirected, finite graph with vertex set V (G) and edge set E(G). A k-dimensional box is a Cartesian product of closed intervals [a1, b1]× [a2, b2]× · · · × [ak, bk]. The boxicity of G, box(G) is the minimum integer k such that G can be represented as the intersection graph of k-dimensional boxes, i.e. each vertex is mapped to a k-dimensional box and two vertices are adjacent...

We outline a method for practical use of an interactive system (APL) to compute the homology of finite partially ordered sets. 1. Prerequisites. All partially ordered sets (posets) are assumed finite. Given a poset , we say that b covers a if b > a and a g c ^ h implies a = c or b = c. Since we deal with finite posets, the order relation can be obtained as the reflexive, transitive clos...

In 2001, the notion of a fuzzy poset defined on a set X via a triplet (L,G, I) of functions with domain X ×X and range [0, 1] satisfying a special condition L+G+ I = 1 is introduced by J. Negger and Hee Sik Kim, where L is the ‘less than’ function, G is the ‘greater than’ function, and I is the ‘incomparable to’ function. Using this approach, we are able to define a special class of fuzzy poset...

We present a technique for destroying stationary subsets of Pκκ using partial square sequences. We combine this method with Gitik’s poset for changing the cofinality of a cardinal without adding bounded sets to prove a variety of consistency results concerning saturated ideals and the set S(κ, κ+). In this paper we continue our study of consistency results concerning the set S(κ, κ) = {a ∈ Pκκ ...