In mathematics, a differential poset is a partially ordered set (or poset for short) satisfying certain local properties. (The formal definition is given...

figures in algebraic combinatorics, forming the simplest example of a differential poset in the sense of Stanley (1988). It is also closely connected with...

of nodes must be equal but may be greater than one) the graph of a differential poset. The transitive closure of the Young–Fibonacci graph is a partial...

combinatorial properties; notably, it is the motivating example of a differential poset. There is a deep theory of random partitions chosen according to the...

(transitivity). A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear. By checking these...

the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations. Certain...

arrangement has, besides its face semilattice, a poset of regions, a different one for each region. This poset is formed by choosing an arbitrary base region...

refers to the primal and dual. For example, the dual poset of the dual poset is exactly the original poset, since the converse relation is defined by an involution...

the reduced homology of a bounded finite poset is another generalization, important in combinatorics. A poset is "bounded" if it has smallest and largest...

closed, or, again equivalently, if the open sets are the upper sets of a poset. Almost discrete A space is almost discrete if every open set is closed...

required explicitly. A directed subset of a poset is not required to be downward closed; a subset of a poset is directed if and only if its downward closure...

studied with Stone's theorem; this is a consequence of the duality between posets and Boolean algebras. On regular lattices, the operator typically has both...

physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model...

general form, a hierarchy is a partially ordered set or poset. The system in this case is the entire poset, which is constituted of elements. Within this system...

Functionally graded elements are used in finite element analysis. A graded poset is a poset P {\displaystyle P} with a rank function ρ : P → N {\displaystyle \rho...

Domain theory a branch that studies special kinds of partially ordered sets (posets) commonly called domains. Donaldson theory the study of smooth 4-manifolds...

of all C-relations, all first-order reducts of the universal homogenous poset, all first-order reducts of homogenous undirected graphs, all first-order...

...22....5S. doi:10.1007/s41114-019-0023-1. Thus, the causal structure poset (M, ≺) of a future and past distinguishing spacetime is equivalent to its...

(1991), p. 75. Enderton (1977), p. 79. For a version that applies to any poset with the descending chain condition, see Bergman (2005), p. 100 Enderton...

Very Early Universe: Abandoning Einstein for a Discretized Three–Torus Poset.A Proposal on the Origin of Dark Energy". Gravitation and Cosmology. 19...

Very Early Universe: Abandoning Einstein for a Discretized Three–Torus Poset.A Proposal on the Origin of Dark Energy". Gravitation and Cosmology. 19...

{S}}(A)=\{001,100,000,110,00*,*00,1*0,**0,*0*,***,\epsilon _{*}\}} The poset ( S ( A ) , ≤ ) {\displaystyle ({\mathcal {S}}(A),\leq )} always forms a...

identity in an enriched category. Since R ∗ {\displaystyle R^{*}} is a poset, all diagrams that are required for an enriched category commute automatically...

{\mathcal {C}}} . A continuity space is a generalization of metric spaces and posets, which uses the concept of quantales, and that can be used to unify the...

given kind; usually it is required that L {\displaystyle L} be at least a poset or lattice. These are usually called L-fuzzy sets, to distinguish them from...

distance. In fact, the interleaving distance is the terminal object in a poset category of stable metrics on multidimensional persistence modules in a...

surjection followed by an injection. Examples are the ordinal α considered as a poset and hence a category. The opposite R° of a Reedy category R is also a Reedy...

"Graph Products Revisited: Tight Approximation Hardness of Induced Matching, Poset Dimension and More". Proceedings of the 2013 Annual ACM-SIAM Symposium on...