In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its...

sets, allow also the insertion and deletion of elements from the set. A multiset is a special kind of set in which an element can appear multiple times...

mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial...

revision of the C++ standard: unordered_set, unordered_map, unordered_multiset, unordered_multimap. Each of these containers differ only on constraints...

is equal to the number of multisets of size k − 1 taken from a set of size n + 1, or equivalently, the number of multisets of size n taken from a set...

number of distinct elements in a multiset. Calculating the exact cardinality of the distinct elements of a multiset requires an amount of memory proportional...

which repetition is allowed, the terms k-combination with repetition, k-multiset, or k-selection, are often used. If, in the above example, it were possible...

k-tuples over S is n k . {\displaystyle n^{k}.} If M is a finite multiset, then a multiset permutation is an ordered arrangement of elements of M in which...

containers are defined in the current revision of the C++ standard: set, map, multiset, multimap. Each of these containers differ only on constraints placed on...

An amenable number is a positive integer for which there exists a multiset of as many integers as the original number that both add up to the original...

to a multiset of elements. A multiset is a generalization of the notion of a set in which an element can occur more than once. Define the multiset union...

type the data is Container List Tuple Associative array, Map Multimap Set Multiset (bag) Stack Queue (example Priority queue) Double-ended queue Graph (example...

growing family of spaces. Formally, a persistence barcode consists of a multiset of intervals in the extended real line, where the length of each interval...

"relation"; although there is the difference in that a table is usually a multiset (bag) of rows where a relation is a set and does not allow duplicates....

series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of 7. 886 = 2 × 443, the Mertens function...

The multiset path ordering (>) can be defined as follows: where (≥) denotes the reflexive closure of the mpo (>), { s1,...,sm } denotes the multiset of...

frequently in general. Like the bag-of-words model, it models a document as a multiset of words, without word order. It is a refinement over the simple bag-of-words...

thought of as signed multisets containing finitely many elements of B {\displaystyle B} , with the multiplicity of an element in the multiset equal to its coefficient...

In mathematics, the prime signature of a number is the multiset of (nonzero) exponents of its prime factorization. The prime signature of a number having...

The standard associative containers are set, multiset, map, multimap, hash_set, hash_map, hash_multiset and hash_multimap. There are also container adaptors...

properties Commutative? Idempotent? Details Ordered? Unique items? List No No Free monoid Yes No Finite multiset Yes No No No Finite set Yes Yes No Yes...

choose k elements from a set of n elements if repetitions are allowed. See Multiset. There are ( n + k k ) {\displaystyle {\tbinom {n+k}{k}}} strings containing...

mathematics, a Stirling permutation of order k is a permutation of the multiset 1, 1, 2, 2, ..., k, k (with two copies of each value from 1 to k) with...

applied to the nth slot. This creates multisets in the unlabelled case and sets in the labelled case (there are no multisets in the labelled case because the...

whose pitches can be expressed as products of some of the members of some multiset of generating prime factors. Powers of two are usually ignored, because...

mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S...

any multiset of 2n − 1 integers has a subset of size n the sum of whose elements is a multiple of n, but that the same is not true of multisets of size...

Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10 678 = 2 × 3 × 113, sphenic number, nontotient,...

tilings of a 12-gon 909 = 32 × 101, number of non-isomorphic aperiodic multiset partitions of weight 7 910 = 2 × 5 × 7 × 13, Mertens function(910) returns...

Empirical distribution function Law of large numbers Multiset multiplicity, analogous to frequency in multiset theory Probability density function Probability...