The free distributive lattices of monotonic Boolean functions on 0, 1, 2, and 3 arguments, with 2, 3, 6, and 20 elements respectively (move mouse over right diagram to see description)
In mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number M(n) is the number of monotone boolean functions of n variables. Equivalently, it is the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements.
Accurate asymptotic estimates of M(n) and an exact expression as a summation are known.[1] However Dedekind's problem of computing the values of M(n) remains difficult: no closed-form expression for M(n) is known, and exact values of M(n) have been found only for n ≤ 9 (sequence A000372 in the OEIS).
mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekindnumber M(n) is...
Wilhelm Richard Dedekind [ˈdeːdəˌkɪnt] (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract...
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors...
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind (but previously considered by Joseph Bertrand), are а method of construction...
a Dedekind ring (or Dedekind domain), in honor of Richard Dedekind, who undertook a deep study of rings of algebraic integers. For general Dedekind rings...
of the Dedekind eta function. They have subsequently been much studied in number theory, and have occurred in some problems of topology. Dedekind sums have...
Weierstrass (by his pupil E. Kossak), Eduard Heine, Georg Cantor, and Richard Dedekind was brought about. In 1869, Charles Méray had taken the same point of departure...
ordered field that is Dedekind complete. Here, "completely characterized" means that there is a unique isomorphism between any two Dedekind complete ordered...
In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function. We start...
In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function (which...
natural-number arithmetic within this second class of definitions. In 1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic...
order of the group, which is finite, is called the class number of K. The theory extends to Dedekind domains and their fields of fractions, for which the...
axiom Dedekind completeness Dedekind cut Dedekind discriminant theorem Dedekind domain Dedekind eta function Dedekind function Dedekind group Dedekind number...
theory, a Dedekind group is a group G such that every subgroup of G is normal. All abelian groups are Dedekind groups. A non-abelian Dedekind group is...
is still an unsolved problem in number theory despite later contributions by other researchers. Richard Dedekind's study of Lejeune Dirichlet's work...
"gaps" (in Dedekind's terminology) or "missing points" in the real number line. This contrasts with the rational numbers, whose corresponding number line has...
{\displaystyle \mathbb {R} \cup \left\{-\infty ,+\infty \right\}.} It is the Dedekind–MacNeille completion of the real numbers. When the meaning is clear from...
and b) or (a and c) or (b and c)). The number of such functions on n variables is known as the Dedekindnumber of n. SAT solving, generally an NP-hard...
constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals (see Construction of the real numbers). The...
lattice is a free distributive lattice, with a Dedekindnumber of elements. More generally, counting the number of antichains of a finite partially ordered...
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that...
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci...
mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...
Eduard Heine (Crelle's Journal, 74), Georg Cantor (Annalen, 5), and Richard Dedekind. Méray had taken in 1869 the same point of departure as Heine, but the...
Rubin, use the term transfinite cardinal to refer to the cardinality of a Dedekind-infinite set in contexts where this may not be equivalent to "infinite...
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The free distributive lattices of monotonic Boolean functions on 0, 1, 2, and 3 arguments, with 2, 3, 6, and 20 elements respectively (move mouse over right diagram to see description)