We introduce a class of posets, which includes both ribbon posets (skew shapes) and $d$-complete such that their number linear extensions is given by determinant matrix whose entr...

The jeu de taquin process produced a standard Young tableau from a skew standard Young tableau by shifting its entries to the northwest. We generalize this process to posets: certain partial numberings of any poset are shifted upward. A poset is said to have the jeu de taquin property if the numberings resulting from this process do not depend upon certain choices made during the process. Young...

We develop a new approach for establishing the Macaulayness of posets representable as cartesian powers of other posets. This approach is based on a problem of constructing an ideal of maximum rank in a poset. Using the relations between the maximum rank ideal problem and the edge-isoperimetric problem on graphs we demonstrate an application of our approach to specification of all posets with a...

We investigate a class of linear error correcting codes in relation with the order polytopes. In particular we consider polytopes tree posets and bipartite posets. calculate parameters associated toric variety codes.

The concept of a Kleene algebra (sometimes also called lattice) was already generalized by the first author for non-distributive lattices under name pseudo-Kleene algebra. We extend these concepts to posets and show how (pseudo-)Kleene can be characterized identities implications assigned commutative meet-directoids. Moreover, we prove that Dedekind-MacNeille completion poset is finite Further,...

In this paper we find new classes of posets which generalize the d-complete posets. In fact the d-complete posets are classified into 15 irreducible classes in the paper “Dynkin diagram classification of λ-minuscule Bruhat lattices and of d-complete posets” (J. Algebraic Combin. 9 (1999), 61 – 94) by R. A. Proctor. Here we present six new classes of posets of hook-length property which generali...

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and...

We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven in [4, 5, 7]. We show that these identities result from a signed differential poset...

The closed cone of flag vectors of Eulerian partially ordered sets is studied. It is completely determined up through rank seven. HalfEulerian posets are defined. Certain limit posets of Billera and Hetyei are half-Eulerian; they give rise to extreme rays of the cone for Eulerian posets. A new family of linear inequalities valid for flag vectors of Eulerian posets is given.