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...

R. Redheffer described an n×n matrix of 0’s and 1’s the size of whose determinant is connected to the Riemann Hypothesis. We describe the permutations that contribute to its determinant and its permanent in terms of integer factorizations. We generalize the Redheffer matrix to finite posets that have a 0 element and find the analogous results in the more general situation.

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 following theorem is due to Dilworth [12]: Let P be a partially ordered set. If the maximal number of elements in an independent subset (anti-chain) of P is k, then P is the union of k chains (cliques). In this article we formalize an elegant proof of the above theorem for finite posets by Perles [17]. The result is then used in proving the case of infinite posets following the original pro...

The symmetric group S(n) is partially ordered by Bruhat order. This order is extended by L. Renner to the set of partial injective functions of {1, 2, . . . , n} (see, Linear Algebraic Monoids, Springer, 2005). This poset is investigated by M. Fortin in his paper The MacNeille Completion of the Poset of Partial Injective Functions [Electron. J. Combin., 15, R62, 2008]. In this paper we show tha...

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,...