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Results tagged with co.combinatorics
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user 919
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
4
votes
Accepted
Are parabolic Kazhdan-Lusztig polynomials truncations of the usual Kazhdan-Lusztig polynomials?
A quick answer for which standard health warnings apply.
For your first question, the answer is positive, as follows (for example) from my paper with Libedinsky here: https://arxiv.org/abs/1702.00459
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- 6,162
8
votes
Combinatorial constructions found by computer
There is a beautiful story involving the faithfulness question of the Burau representation of the braid group.
Moody showed that the Burau representation is unfaithful if $n$ (the number of strands) …
14
votes
0
answers
617
views
Chasing a 1950s thesis from the University of Dhaka on block designs
On behalf of a friend I am searching for a thesis on block designs from the 1950s. The details are below.
Author: Qazi Motahar Husein (Sometimes Husain or Hussein).
Title of the Thesis: Symmetrical …
- 6,162
4
votes
Intersection homology for toric varieties
There is a simple and beautiful description in terms of commutative algebra (repeatedly calculating global sections and taking a projective cover). The work of Braden-MacPherson cited by Alexander is …
- 6,162
4
votes
Subexpressions of reduced words in Coxeter groups
I have found a much more efficient way of solving this problem on computer. Having asked the question I guess I should provide a brief account. However I feel like the algorithm is technical and not v …
- 6,162
9
votes
2
answers
894
views
Subexpressions of reduced words in Coxeter groups
Let $\underline{w} = [s_1, s_2, \dots ,s_n]$ be a reduced expression in a Coxeter group $W$. Given $x$ in $W$ one can consider the set $\Pi(\underline{w},x)$ consisting of all subexpressions of $\unde …
- 6,162
25
votes
Is Soergel's proof of Kazhdan-Lusztig positivity for Weyl groups independent of other proofs?
Perhaps I can supplement Jim's answer a little.
In the paper "Kazhdan-Lusztig-Polynome und unzerlegbare Bimoduln uber Polynomringen" Soergel shows that there are certain graded indecomposable bimodul …
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