In mathematics, a differential poset is a partially ordered set (or poset for short) satisfying certain local properties. (The formal definition is given below.) This family of posets was introduced by Stanley (1988) as a generalization of Young's lattice (the poset of integer partitions ordered by inclusion), many of whose combinatorial properties are shared by all differential posets. In addition to Young's lattice, the other most significant example of a differential poset is the Young–Fibonacci lattice.
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In mathematics, a differentialposet is a partially ordered set (or poset for short) satisfying certain local properties. (The formal definition is given...
combinatorial properties; notably, it is the motivating example of a differentialposet. 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...
Möbius inversion can be represented by convolution with a function on the poset, called the Möbius function μ; for the difference operator, μ is the sequence...
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...
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...
the reduced homology of a bounded finite poset is another generalization, important in combinatorics. A poset is "bounded" if it has smallest and largest...
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...
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...
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...
identity in an enriched category. Since R ∗ {\displaystyle R^{*}} is a poset, all diagrams that are required for an enriched category commute automatically...
Domain theory a branch that studies special kinds of partially ordered sets (posets) commonly called domains. Donaldson theory the study of smooth 4-manifolds...
a power set, the positive reals, the irrational numbers, or a forcing poset. U+1D561 𝕡 Q {\displaystyle \mathbb {Q} } U+211A ℚ Represents the set of...
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...
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...
distance. In fact, the interleaving distance is the terminal object in a poset category of stable metrics on multidimensional persistence modules in a...
120, Devine et al. p. 75 Enderton p. 79 For a version that applies to any poset with the descending chain condition, see Bergman p. 100. Enderton (p. 79)...
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...
{\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...
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...
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