All Questions
8 questions
32
votes
1
answer
2k
views
Is this formal noncommutative power series identity known?
I recently discovered the following cute formal noncommutative power series identity: if $(x_i)_{i \in I}$ is some finite collection of noncommuting variables, then the formal power series
$$ 1 + \...
- 114k
11
votes
2
answers
606
views
Temperley-Lieb algebras for other Weyl groups?
The Temperley-Lieb algebra has the same generators as the $S_n$ group algebra, and the same commuting relations, but its other relations are different. A nice diagrammatic interpretation can be seen ...
- 27.8k
5
votes
1
answer
418
views
The formula for a perhaps basic identity (move from stackexchange)
The following question is moved from math stackexchange. It seems that this is not a popular question, but I really want to know the answer so I moved it to here. The question reads as follows.
We ...
- 1,173
4
votes
1
answer
236
views
Solving equations in the Brauer algebra
(First asked in MSE)
The Brauer algebra $B_n(x)$ is an algebra of matchings whose product is described here.
Given $A$ and $B$ two elements of $B_n(x)$, and given an integer $m$, there are in ...
- 1,549
3
votes
0
answers
116
views
A theory of refined h- and f-polynomials for the permutahedra, associahedra, noncrossing partitions, and tropical Grassmannians (references)
Looking for references (insights) on a theory encompassing a notion of refined face polynomials and their associated refined h-polynomials that are generalizations of the relation between ordinary f-...
- 10.5k
3
votes
0
answers
86
views
$\mathbb Z$-torsion for some quadratically presented Lie rings
$\newcommand{\Z}{\mathbb{Z}}$
I asked this question on MSE but no answer so far, so I'm also asking it here.
Let $L$ be a Lie ring (a Lie algebra over $\Z$) with generators $x_1,\dots,x_n$ and ...
- 8,524
2
votes
2
answers
77
views
Reference request for a subfamily of regular graphs
[Repost of same question math stack exchange which got no answers]
I'm looking for literature on the following family of graphs:
Call a regular graph $G=(V,E)$ (of regularity degree $d$) nice if there ...
- 21
1
vote
2
answers
301
views
A question on linear recurrence
Let $(a_{i})$ be an increasing sequence of positive integers given by a linear recurrence $a_{i+n}=c_{n}a_{i+n-1}+\dots +c_{1}a_{i}$ with $c_{i}\in\{-1,0,1\}$ and $a_{i}=2^{i}$ for $i=1,\dots n$ such ...
- 1,648