We construct a family of posets, called signed Birkhoff posets, that may be viewed as signed analogs of distributive lattices. Our posets are generally not lattices, but they are shown to posses many combinatorial properties corresponding to well known properties of distributive lattices. They have the additional virtue of being face posets of regular cell decompositions of spheres. We give a c...

Lacking an explicit formula for the numbers T0(n) of all order relations (equivalently: T0 topologies) on n elements, those numbers have been explored only up to n = 13 (unlabeled posets) and n = 15 (labeled posets), respectively. In a new approach, we used an orderly algorithm to (i) generate each unlabeled poset on up to 14 elements and (ii) collect enough information about the posets on 13 e...

We characterize the linear inequalities satisfied by flag f -vectors of all finite bounded posets. We do the same for semipure posets. In particular, the closed convex cone generated by flag f -vectors of bounded posets of fixed rank is shown to be simplicial, and the closed cone generated by flag f -vectors of semipure posets of fixed rank is shown to be polyhedral. The extreme rays of both of...

the finite set of minimal elements is delivered following [1]. This is being achieved via adjacency and zeta matrix description of bipartite digraphs chains the representatives of graded posets. The bipartite digraphs elements of such chains amalgamate to form corresponding cover relation graded poset digraphs with corresponding adjacency matrices being amalgamated throughout natural join as sp...

Given a permutation $\tau$ defined on set of combinatorial objects $S$, together with some statistic $f:S\rightarrow \mathbb{R}$, we say that the triple $\langle S, \tau,f \rangle$ exhibits homomesy if $f$ has same average along all orbits in $S$. This phenomenon was observed by Panyushev (2007) and later studied, named extended Propp Roby (2013). studied order ideals product two chains, well k...

We consider the class Pn of labeled posets on n elements which avoid certain three-element induced subposets. We show that the number of posets in Pn is (n+1) by exploiting a bijection between Pn and the set of regions of the arrangement of hyperplanes in R of the form xi&xj=0 or 1 for 1 i< j n. It also follows that the number of posets in Pn with i pairs (a, b) such that a<b is equal to the nu...

We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of two-dimensional countable subshifts with interesting properties. We present an SFT whose iterated derivatives are maximally complex from the computational point ...

One of central issues in extremal set theory is Sperner's theorem and its generalizations. Among such generalizations is the best-known BLYM inequality and the Ahlswede--Zhang (AZ) identity which surprisingly generalizes the BLYM into an identity. Sperner's theorem and the BLYM inequality has been also generalized to a wide class of posets. Another direction in this research was the study of mo...

the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it&apos;s proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...

We introduce a special type of graph embedding called book embedding and apply it to posets. A book embedding scheme for bipartite graphs is given, and is used to extend the embeddings to general k-partite graphs. Finally, we view the Hasse diagram of a poset as a directed k-partite graph and use this scheme to derive a book embedding for arbitrary posets. Using this book embedding scheme, we a...