# Questions tagged [multisets]

For questions about or related to multisets, a notion similar to sets with the difference that elements can be repeated.

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### cardinality of a multiset

Multiset Notation First, let's agree on the following representation of a multiset (a set that allows duplications). A multiset Multiset is represented as a pair <...
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### How to solve "linear multiset equations"?

I have a bunch of linear forms in the same number of variables, with the number of linear forms much larger than the number of variables. Say, they are $\ell_i(x_1,...,x_n)=l_{i1}x_1+...+l_{in}x_n$, ...
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### Elegant notation for partial intersections in cartesian products?

Let $A⊆X×Y$ $A$ be a multi-set over $X×Y$ $A∈⋃_{n∈ℕ}(X×Y)^n$ Anyway, $A$ is a collection of tuples $(x, y)$, potentially with duplicates in cases (2) and (3). Given $F⊆X$, I am looking for an ...
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### Notation for collection of elements that may contain duplicates [closed]

I want to represent document D as a collection of words. I was inclined to do this with: D = {w_1, w_2, ... }. However, the ...
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### Combinatorics of a Single-Chiral-Center Molecule

I'll preface with the fact that I'm currently studying undergrad biophysics, so I don't have much background in math. What I want to find: a combinatorics approach to calculating the number of unique ...
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### How to get count and generation of all the unordered pairs for multisets?

Say for $N$ sets assuming $N = 3$ with all distinct elements like in the below eg, $A = \lbrace 1,2,3\rbrace$; $B = \lbrace 4,5\rbrace$ and $C = \lbrace 6\rbrace$ How to find all the unordered pairs ...
1 vote
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### What is a partial multiset?

A. Rabinovich, and B. A. Trakhtenbrot, in their Behavior Structures and Nets paper, uses the expression "partial multiset" without defining it. In context, they have an alphabet $\Sigma$, a ...
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### Formula for calculating the combination of a multiset taken r at a time? [duplicate]

If we have a multiset S = {a,a,b,b,b,c,d} How to calculate all possible combinations if we take r items at a time? For example if r = 3 then the combinations will ...
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### What is the growth rate of OEIS A347913?

OEIS A347913 is an extremely interesting sequence about multisets of integers. It is defined as the number of multisets one can get starting with a multiset of $n$ zeros and "splitting", ...
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### Is a multiset an element of itself?

I know that a set cannot be an element of itself, but I don’t find anything about multisets. So, my question is: is a multiset an element of itself?
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### Distributive property for signed multiset

I'm reading through Wayne Blizard's introduction to signed multisets, which says at the bottom of page 9 that additive union distributes over intersection. I see how this is true for normal (non-...
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### Given the length of a word, knowing there are no consecutive letters, and knowing how many of each letter, how can I find the number of permutations?

To start, I am not a mathematician, so please keep answers and notations to something that any high school graduate could understand. I am a Software Performance Engineer by trade and am looking for ...
1 vote
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### Polynomials considered as multisets of roots: extend polynomial addition and derivation to $\mathbb{R}^n$

Informal context In $\mathbb{C}[X]$, all polynomials are split, so monic polynomials are in bijection with the multisets of their roots, i.e. the finite sub-multisets of $\mathbb{C}$. Polynomial ...
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