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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

"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....

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...

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

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...

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

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...

problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such...

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...

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...

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...

Queue Double-ended queue Priority queue Double-ended priority queue Set Multiset Disjoint-set Arrays Bit array Circular buffer Dynamic array Hash table...

considered an unordered pair, although today, most would say that {a, a} is a multiset. It is typical to use the term unordered pair even in the situation where...

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

{\displaystyle S(4,3)} can be thought of as a multiset of cardinality n = 4 {\displaystyle n=4} ; the elements of such multiset are taken from the set { 1 , 2 , 3...

computer scientist, known e.g. for the Dershowitz–Manna ordering and the multiset path ordering used to prove termination of term rewrite systems. He obtained...