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...

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

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...

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...

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...

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...

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

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...

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...

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

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...

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...

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...

mathematics, the Dershowitz–Manna ordering is a well-founded ordering on multisets named after Nachum Dershowitz and Zohar Manna. It is often used in context...

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...

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...

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...

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

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...

"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....

bars (combinatorics), a graphical method used to derive the formula for multiset coefficients and other combinatorial theorems Stars and Bars (novel), a...

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...

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

logical function NOT. and in APL it additionally represents the dyadic multiset function without (set difference).: 258  In C the tilde character is used...

integer polymatroid. In this sense, a polymatroid can be considered a multiset analogue of a matroid. Let E {\displaystyle E} be a finite set. If u ,...

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

i and j have the same number of digits and the multiset of the digits of n coincides with the multiset of the digits of i and j.)". The On-Line Encyclopedia...

_{i}^{\,{\text{th}}}} roots of unity. The multiset union of the L i {\displaystyle L_{i}} is then the multiset of eigenvalues of P. Since writing ρ P {\displaystyle...

problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} ,...