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Jan
23
comment How to fill up $(0,1)$ with disjoint closed intervals all total measure one
Do you really think that editing your question and unselecting my answer will motivate me to answer your new question?
Jan
22
comment Young Tableaux Generalizing
@Yadnarav3 The irreducible representations of the symmetric group happen to have (vector space) bases that are indexed by Young tableaux of a given shape. Therefore, counting the Young tableaux means that you are calculating the dimension of a particular representation. The formula really does exactly the enumeration you want, but it also has an algebraic meaning. If you are interested, you can, for example, read "The Symmetric group" by Sagan or "Young tableaux" by Fulton.
Jan
21
comment How do I convince my students that the choice of variable of integration is irrelevant?
For @HelloGoodbye s problem, I would point out that the definition of a function contains an implicit "for all" that is omitted by convention and/or laziness, and that it is the "for all" that makes the variable a local variable.
Jan
21
comment How do I convince my students that the choice of variable of integration is irrelevant?
It is a good idea to introduce some language that one uses every time the problem occurs (whether with functions, limits, sums or integrals). Since my students also study programming, I always point out which variables are local variables and which ones are global variables and why this should make them avoid the particular error that they just wanted to commit.
Jan
20
comment Show $\binom{n}{k}\binom{k}{a} = \binom{n}{a}\binom{n-a}{k-a}$ by block-walking interpretation of Pascal's triangle
@IDentity You are not the one who set the bounty.
Jan
20
comment Taking Seats on a Plane: The General Case
@user117432 This one assumption is not particularly strong, it is more a question of being a case where it is not clear what outcome you really want to measure as this puzzle is often worded "find their seats empty" which is not the same thing to "sit on their seat".
Jan
20
comment Taking Seats on a Plane: The General Case
@user117432 I still do not know what you are talking about. The only assumption is that the $i$ last passengers are disjoint from the $m$ forgetful people. I did NOT assume that the forgetful people board the plane first.
Jan
20
awarded  Enlightened
Jan
20
awarded  Nice Answer
Jan
17
reviewed Close Colored Picture for Equivalence Classes, Relations, Partitions, ..
Jan
17
reviewed Close Probability question based on cards
Jan
17
comment Probability question based on cards
You should tell us what a "deck" is. Also, do you know what the probability is to get a jack on the first try?
Jan
17
comment Integrating two equations that equal, what happens to the constant on one of the sides?
The difference of two unknown constants is not more general than a single unknown constant.
Jan
17
comment In how many ways can you arrange a circle of partners so that no partners are touching?
@KBusc Your small numbers indicate that you want to regard rotated seatings as equivalent, but you should say so explicitly.
Jan
17
answered Painting a circle that is divided into $6$ pieces
Jan
16
answered Binomial coefficient manipulation
Jan
16
answered Proving $\sum\limits_{k=0}^{n} (-1)^{k} \binom{n}{k} = 0$
Jan
16
comment Show $\binom{n}{k}\binom{k}{a} = \binom{n}{a}\binom{n-a}{k-a}$ by block-walking interpretation of Pascal's triangle
The literal interpretation of the question gives one of the existing answers, a more refined interpretation gives the other answer. Other approaches to the identity certainly exist, but they do not seem to answer the question, so presumably the bounty wants to modify the question a bit.
Jan
16
comment Generally true or false? $\lim_{n\to\infty} f(g(n)) \ne f(\lim_{n\to\infty} g(n)) $
@hardbutfun Hello, you have set a bounty on another question but you did not really explain what you want.
Jan
16
comment Show $\binom{n}{k}\binom{k}{a} = \binom{n}{a}\binom{n-a}{k-a}$ by block-walking interpretation of Pascal's triangle
I have no idea what this bounty is looking for.