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...

To an extended generalized permutohedron we associate the weighted integer points enumerator, whose principal specialization is f-polynomial. In case of poset cones it refines Gessel?s P-partitions enumerator. We show that this enumerator a quasisymmetric function obtained by universal morphism from Hopf algebra posets.

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.

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...

We study signed differential posets, a signed version of Stanley’s 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 [3, 4, 6]. We show that these identities result from a signed differen...

First, Cogis and Habib (RAIRO Inform. 7Mor. 13 (1979), 3-18) solved the jump number problem for series-parallel partially ordered sets (posets) by applying the greedy algorithm and then Rival (Proc. Amer. Math. Sot. 89 (1983). 387-394) extended their result to N-free posets. The author (Order 1 (1984), 7-19) provided an interpretation of the latter result in the terms of arc diagrams of posets ...

This thesis contains five papers divided into two parts. In the first part, Papers I–IV, we study polynomials within the field of combinatorics. Here we study combinatorial properties as well as the zero distribution of the polynomials in question. The second part consists of Paper V, where we study correlating events in randomly oriented graphs. In Paper I we give a new combinatorial interpret...

A poset is (3 + 1)-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets are the subject of the (3 + 1)-free conjecture of Stanley and Stembridge. Recently, Lewis and Zhang have enumerated graded (3+1)-free posets, but until now the general enumeration problem has remained open. We enumerate all (3 + 1)-free posets by giving a decomposit...