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1d
answered Number of double cosets of a Young subgroup
1d
awarded  Explainer
Sep
25
comment Why is there a connection between enumerative geometry and nonlinear waves?
Some other references are the five arXiv papers by Yuji Kodama and Lauren Williams.
Sep
17
answered Pictures of the von Neumann polytope
Sep
13
comment Flag complexes that are shellable but not vertex decomposable
Proposition 6.8(i) of arxiv.org/pdf/1303.2070.pdf gives an example of a nonshellable triangulation of a 3-ball whose barycentric subdivision is vertex-decomposable. This suggests that there might be a nonshellable triangulation of a 3-ball whose barycentric subdivision is shellable but not vertex-decomposable.
Sep
9
awarded  co.combinatorics
Sep
9
answered Counting cyclic binary sequences of length $n$ where ones appear in blocks of length at least $k$
Sep
9
revised Counting cyclic binary sequences of length $n$ where ones appear in blocks of length at least $k$
corrected spelling in title
Aug
16
comment Set of distinct real numbers such that all combination of sums are distinct
In fact, if we want the condition to hold for all $p$, then linear independence over $\mathbb{Q}$ is necessary and sufficient.
Aug
15
awarded  Famous Question
Aug
11
awarded  Nice Answer
Jul
19
answered General criterion to find a Z-basis in a fixed generating subset
Jul
17
comment Combinatorial interpretation of composition of power series?
For the general theory of the formal power series identity $f(f(t))=t$, see Enumerative Combinatorics, vol. 1, Exercise 1.168.
Jul
14
comment Counting representations of $k[x,y]$ when $k$ is finite
Is it just a coincidence that $r_n(1)$ is the middle coefficient of $(1+x+x^2)^n$ for $1\leq n\leq 4$?
Jul
14
comment counting the number of ordered pairs in a permutohedron
People have looked at this kind of question, but I believe your particular question is open. See for instance Exercise 3.185 of *Enumerative Combinatorics", vol. 1. Your question is closely related to mathoverflow.net/questions/173042, since the number of pairs $\tau\leq\sigma$ is equal to $\sum_\sigma \#[\mathrm{id},\sigma]$.
Jul
14
awarded  Great Answer
Jul
13
awarded  Necromancer
Jul
12
answered What is natural about the well-known bijection between conjugacy classes and irreps of a symmetric group?
Jul
11
answered Sums of subsets of $\mathbb{Z}/n\mathbb{Z}$
Jul
6
comment Ordinary Generating Function for Bell Numbers
As an aside, let $G(t)=\sum_{n\geq 0}B_nt^n$. Then the solution to Exercise 1.111 of Enumerative Combinatorics, vol. 1, shows that $(1-t)G(t(1-t))$ is the ordinary generating function for the number of partitions of $1,2,\dots,n$ such that no block is an interval $a,a+1,\dots,b$ (including the case $a=b$).