In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free...

the notion of a K-trivial set. These sets are anti-random in that all initial segment is logarithmically compressible (i.e., K ( w ) ≤ K ( | w | ) + b {\displaystyle...

factor of 42. The non-trivial divisors of 6 are 2, −2, 3, −3. The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. The set of all positive divisors...

K {\displaystyle K} if the elements of S {\displaystyle S} do not satisfy any non-trivial polynomial equation with coefficients in K {\displaystyle K}...

trivial bundle of rank k {\displaystyle k} over X {\displaystyle X} . Given a vector bundle E → X {\displaystyle E\to X} of rank k {\displaystyle k}...

transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some non-trivial element fixes a point. They are named...

called the direct sum of a finite set of subgroups {Hi} if each Hi is a normal subgroup of G, each Hi has trivial intersection with the subgroup ⟨{Hj :...

a field extension L / K acts on the field L but has only a trivial action on elements of the subfield K. Subgroups of Gal(L / K) correspond to subfields...

X | : X  is a non-trivial cutset } . {\displaystyle \kappa _{1}(G)=\min\{|X|:X{\text{ is a non-trivial cutset}}\}.} A non-trivial edge-cut and the...

their corresponding computational machine implementations are equally trivial. It can be worth it to add additional interpretation rules, allowing for...

j, −j, k, −k}, is {1, −1}. The center of the symmetric group, Sn, is trivial for n ≥ 3. The center of the alternating group, An, is trivial for n ≥ 4...

algebraic number field K {\displaystyle K} is the quotient group J K / P K {\displaystyle J_{K}/P_{K}} where J K {\displaystyle J_{K}} is the group of fractional...

implies trivially that (b, –a) is a linear relation between a and b. Therefore, given a generating set g 1 , … , g k {\displaystyle g_{1},\dots ,g_{k}} of...

algebraic variety. The earliest work on a non-trivial Grassmannian is due to Julius Plücker, who studied the set of projective lines in real projective 3-space...

In quantum information theory, the no low-energy trivial state (NLTS) conjecture is a precursor to a quantum PCP theorem (qPCP) and posits the existence...

include permutations with fixed points in addition to at most one non-trivial cycle. In cycle notation, cyclic permutations are denoted by the list of...

partition.) For any non-empty set X, P = { X } is a partition of X, called the trivial partition. Particularly, every singleton set {x} has exactly one partition...

the product space to the first factor. This is called a trivial bundle. Examples of non-trivial fiber bundles include the Möbius strip and Klein bottle...

departmentID} is the trivial superkey. If attribute set K is a superkey of relation R, then at all times it is the case that the projection of R over K has the same...

because of the covering set {7, 13, 31, 37, 97}. Besides, these k are not trivial since gcd(k + 1, 6 − 1) = 1 for these k. (The Riesel base 6 conjecture...

∑ k 1 > k 2 > ⋯ > k n > 0 k 1 − s 1 k 2 − s 2 ⋯ k n − s n . {\displaystyle \zeta (s_{1},s_{2},\ldots ,s_{n})=\sum _{k_{1}>k_{2}>\cdots >k_{n}>0}{k...

Therefore, there is at least one non-trivial polynomial of degree less than |F| that vanishes on any given set with less than this number of points....

coarsest topology on X is the trivial topology; this topology only admits the empty set and the whole space as open sets. In function spaces and spaces...

{\displaystyle C} itself and the empty set are faces of C {\displaystyle C} ; these are sometimes called the trivial faces of C {\displaystyle C} . An extreme...

involution.) k c k c k c k c S = k c k c S {\displaystyle kckckckcS=kckcS} . (Or equivalently k c k c k c k S = k c k c k c k c c S = k c k S {\displaystyle...

( f k ) {\displaystyle \varphi (f_{1}),\ldots ,\varphi (f_{k})} do not have any non-trivial common zero. This is the case if the maximal homogeneous ideal...

bundle is trivial. By definition, a manifold M {\displaystyle M} is framed if and only if the tangent bundle T M {\displaystyle TM} is stably trivial, meaning...

follows: (S (K (S I)) (S (K K) I) x y) = (K (S I) x (S (K K) I x) y) = (S I (S (K K) I x) y) = (I y (S (K K) I x y)) = (y (S (K K) I x y)) = (y (K K x (I x)...

is a trivial G-module (i.e. the action of G on M is trivial), the second cohomology group H2(G,M) is in one-to-one correspondence with the set of central...

unlike APL, K restricts itself to the ASCII character set (as does another APL variant, J). To allow for this, the set of primitive functions for K is smaller...