The symmetric group Sn acts naturally on the poset of injective words over the alphabet {1, 2, . . . , n}. The induced representation on the homology of this poset has been computed by Reiner and Webb. We generalize their result by computing the representation of Sn on the homology of all rank-selected subposets, in the sense of Stanley. A further generalization to the poset of r-colored inject...

We use the theory of poset resolutions to construct the minimal free resolution of an arbitrary stable monomial ideal in the polynomial ring whose coefficients are from a field. This resolution is recovered by utilizing a poset of Eliahou-Kervaire admissible symbols associated to a stable ideal. The structure of the poset under consideration is quite rich and in related analysis, we exhibit a r...

Brualdi et al. introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Hamming code to be a double-error-correcting perfect P-code. Our study is motivated by this example. In this paper we classify all poset structures which admit the extended binary Hamming code to be a double or triple-error-correcting perfect P-code. © 2004 Elsevier B.V....

Let Q(k, l) be a poset whose Hasse diagram is a regular spider with k+1 legs having the same length l (cf. Fig. 1). We show that for any n ≥ 1 the nth cartesian power of the spider poset Q(k, l) is a Macaulay poset for any k ≥ 0 and l ≥ 1. In combination with our recent results [2] this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices,...

We study differential posets, a family of partially ordered sets discovered by Richard Stanley. In the first half of this paper we present an introduction to poset theory as relevant to differential posets and theorems on the structure and combinatorial properties of differential posets, culminating in the explicit definition of a new differential poset. In the second half we focus on Young’s l...

A t-box representation of a graph encodes each vertex as a box in t-space determined by the (integer) coordinates of its lower and upper corner, such that vertices are adjacent if and only if the corresponding boxes intersect. The boxicity of a graph G is the minimum t for which this can be done; equivalently, it is the minimum t such that G can be expressed as the intersection graph of interva...

The notation and terminology used here are introduced in the following papers: [18], [13], [17], [14], [19], [7], [1], [8], [6], [20], [3], [9], [2], [10], [15], [16], [5], [11], [4], and [12]. Let us observe that there exists a lattice which is finite. Let us mention that every lattice which is finite is also complete. Let L be a lattice and let D be a subset of the carrier of L. The functor D...

We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group. Also we present the poset of Borel congruence classes of anti-symmetric matrices ordered by containment of...

In this paper we study topological properties of the poset of injective words and the lattice of classical non-crossing partitions. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This extends the well-known result that those posets are shellable. Both results rely on a new poset fiber theorem, for doubly homo...

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...