The most powerful feature of categories of posets with directed sups is the ability to solve domain equations such as D ∼= D. A crucial ingredient of this technique is the fact that for certain kinds of diagrams (in particular sequences of “projection pairs”) the limit and colimit are isomorphic. This much is known to everyone in the subject: what appears not to be generally known is (i) that w...

We define posets of types B, C, and D. These encode the matrix forms certain Lie algebras which lie between upper-triangular diagonal matrices. Our primary concern is index spectral theories such type-B, D poset algebras. For an important restricted class, we develop combinatorial formulas and, in particular, characterize corresponding to Frobenius In this latter case show that spectrum binary;...

We describe one-dimensional central measures on numberings (tableaux) of ideals partially ordered sets (posets). As the main example, we study poset $$\mathbb{Z}_+^d$$ and graph its finite ideals, multidimensional Young tableaux; for $$d=2$$ , this is ordinary graph. The are stratified by dimension; in paper give a complete description stratum prove that every ergodic measure uniquely determine...

Abstract A detailed geochronological study was conducted on zircons from a diorite sample of the Posets pluton (Axial Zone, Pyrenees). The extracted igneous constrain emplacement to 302 ± 2 Ma and 301 3 Ma, by means U–Pb sensitive high-resolution ion microprobe (SHRIMP) laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) analyses, respectively. Considering syn- late-tectonic...

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...

The weak order on the symmetric group naturally extends to a lattice on all integer binary relations. We first show that the subposet of this weak order induced by integer posets defines as well a lattice. We then study the subposets of this weak order induced by specific families of integer posets corresponding to the elements, the intervals, and the faces of the permutahedron, the associahedr...

In every dense poset P every maximal antichain S may be partitioned into disjoint subsets S1 and S2 , such that the union of the upset of S1 with the downset of S2 yields the entire poset: U(S1) [ D(S2) = P . To nd a similar splitting of maximal antichains in posets is NP{hard in general.

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...

Possibly the most fundamental combinatorial invariant associated to a finite simplicial complex is its f-vector, the integral sequence expressing the number of faces of the complex in each dimension. The h-vector of a complex is obtained by applying a simple invertible transformation to its f-vector, and thus the two contain the same information. Because some properties of the f-vector are easi...

The Dushnik-Miller dimension of a partially-ordered set P is the smallest d such that one can embed into product linear orders. We prove divisibility order on interval {1,…,n}, equal to (log⁡n)2(log⁡log⁡n)−Θ(1) as n goes infinity. similar bounds for 2-dimension in where poset isomorphic suborder subset lattice [d]. also an upper bound posets bounded degree and show (αn,n] Θα(log⁡n) α∈(0,1). At ...