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...

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}...

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...

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...

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

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...

Trivial File Transfer Protocol (TFTP) is a simple lockstep File Transfer Protocol which allows a client to get a file from or put a file onto a remote...

membership of elements to sets. The task is then to find a minimum cardinality subset of left-vertices that has a non-trivial intersection with each of...

have trivial ideal class groups. If k is a field, then the polynomial ring k[X1, X2, X3, ...] is an integral domain. It has a countably infinite set of...

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...

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...

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...

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 :...

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...

∑ 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...

{\displaystyle H} . When H {\displaystyle H} is the trivial class, twisted K-theory is just untwisted K-theory, which is a ring. However, when H {\displaystyle...

the group has no non-trivial abelian quotients (equivalently, its abelianization, which is the universal abelian quotient, is trivial). In symbols, a perfect...

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...

n=0} and n = 1 {\displaystyle n=1} (the empty set and the singleton set), the symmetric groups are trivial (they have order 0 ! = 1 ! = 1 {\displaystyle...

rational field is not complete with respect to non-trivial absolute values; with respect to the trivial absolute value, the rational field is a discrete...

integer k≥3, the k-set packing problem is a variant of set packing in which each set contains at most k elements. When k=1, the problem is trivial. When k=2...

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...

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...

applied to the data set, this fact remains true over time. Initially when each node is the root of its own tree, it's trivially true. The only case when...

taking the intersection of a fuzzy set with itself is not trivial. It instead defines the m-th power of a fuzzy set, which can be canonically generalized...

of K and the way K it is represented. For example: If K is represented by a set of some m linear inequalities, then SSEP (and hence SMEM) is trivial: given...

maximum independent set; therefore, this trivial algorithm attains a (d-1)-approximation algorithm for the maximum independent set. In fact, it is possible...

collection of sets may have an empty intersection without being disjoint. Additionally, while a collection of less than two sets is trivially disjoint, as...