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...

Trivial Pursuit is a board game in which winning is determined by a player's ability to answer trivia and popular culture questions. Players move their...

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...

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}...

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...

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...

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...

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...

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

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...

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...

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...

{\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...

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...

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...

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...

Galois extension K / k {\displaystyle K/k} , there is a bijection between the set of subfields k ⊂ E ⊂ K {\displaystyle k\subset E\subset K} and the subgroups...

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

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...

characteristic of the trivial bundle is one minus the genus, and the only nontrivial characteristic class is the degree. The subject of K-theory takes its...

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...

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...

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...

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...

generated by S . {\displaystyle S.} Given a vector space V over a field K, the span of a set S of vectors (not necessarily finite) is defined to be the intersection...