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...

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...

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}...

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...

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...

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...

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...

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...

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 :...

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

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...

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...

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...

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...

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...

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...

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

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