Showcasing the stars and bars method for counting type problems in math.

Suma de subconjuntos como particiones. Subset sum as partitions. [ ES / EN ]

[Image 1] Introduction Hey it's a me again @drifter1! Today we continue with Mathematics, and more specifically the branch of "Discrete Mathematics", in order to get into Combinatorics Topics.

[Image 1] Introduction Hey it's a me again @drifter1! Today we continue with Mathematics, and more specifically the branch of "Discrete Mathematics", in order to get into Combinations and

[Image 1] Introduction Hey it's a me again @drifter1! Today we continue with Mathematics, and more specifically the branch of "Discrete Mathematics", in order to get into Combinatorial Principles.

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The Bell numbers count how many ways there are to partition N elements into sets. What if we want to partition the elements into ordered groups instead, as this Quora question asks? For example, {a,b}

Thanks to a video I saw on Youtube, I know now a way to prove both the relations I used in this post. First a few notations: Given a closed simply connected (without holes) domain on the plane, let B >

Suppose we have a two-state cellular automaton using the Moore neighborhood, which counts both orthogonal and diagonal neighbors. How many possible rules are there? With 9 cells total (including the center

If you start at (0,0) and can take one step at a time either north (0,+1) or east (+1,0), how many different ways are there to get to (3,5)? I wanted to augment this answer on Quora with a visual

A K-club on a graph is a subset of the vertices such that the diameter of the induced subgraph is less than or equal to K. "Induced subgraph" just means "pick all the edges which both endpoints

Sol LeWitt's artwork "Incomplete Open Cubes" enumerates all distinct connected sets of edges of the cube which do not collapse into a smaller dimension (a figure that lies in the plane, or a

A "discard tree" is a data structure I invented that is keyed by bitvectors representing K-combinations. It permits us to efficiently find all bitvectors that do not intersect with the search

In abstract terms: Given an N-element set, how many L-element subsets do we need so that every K-element subset is a superset of one of the L-element subsets? Let's express this by saying that the family

A key feature of lowball games such as Razz or Deuce-to-Seven Triple Draw is that all players are competing to make hands using the same set of low cards. Thus it is fairly common that some of the cards

Image source: In my previous post, I introduced some basic concepts in combinatorics. If you haven't read the previous post, you can do so here. Arranging objects when some objects are identical A common

Two Books made freely available by "M.Lothaire" (M.Lothaire is a collective name chosen by the authors). It is all about "combinatorics on words" with theory, algorithms applied to

How many ways are there to place 20 generic balls into 4 unique bins? This is a simple combinatorics question and I'll post a cool way of thinking about the answer tomorrow...leave any guesses in the comments

Combinatorics ”the branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those of graph theory.” – Google Definition I loved

I heard about steemit from my awesome brother Jack, @jacKeown.  He told me it would be a good community for me to become a part of so I plan to post a lot about the things I'm interested in; namely