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Eduard Looijenga provided a scanned version of the letter, which now can be found at http://homepage.univie.ac.at/christian.stump/Deligne_Looijenga_Letter_09-03-1974.pdf (outdated) http://homepage.r …

You want to print a deck of cards of the following type: Each card shows $k$ items out of $n$ different items such that any two cards in the deck share exactly one item. Question: What is the bigg …

Hello, I wonder if anyone has a copy of Deligne's letter to Looijenga from 1974 mentioned as reference [26] in Bessis' paper Finite complex reflection arrangements are $K(\pi,1)$ from 2006, see http: …

Let $V$ be a complex vector space of finite dimension $n$ and let $W$ be a finite unitary reflection group. This is, $W$ is a subgroup of $GL(V)$ generated by reflections, i.e., elements $r \in GL(V)$ …

(in contrary to what I thought first,) here is a proof that the "exchange condition" holds in the following sense. It is based on the root configuration in http://arxiv.org/abs/1111.3349 [1]. Let $(W …

These are several comments rather than an answer: As you write, let $(Q,w,S)$ denote all subwords of $Q$ whose greedy product is $w$ with positions $S$ skipped. I moreover write $(Q,w)$ for w in the …

(This is more of a longer comment without a proper answer to the question.) I assume you mean "An embedding $(W,S) \hookrightarrow (W',S')$ is an injective map from $S$ to the set $T' = \{ w s w^{-1} …

We started writing up combinatorial statistics on http://www.findstat.org . There you already find some (but not yet many) symmetric statistics. People who are interested and would like to contribute …

Mahonian statistics on permutations: A statistic $stat$ is Mahonian if it is equidistributed with the major index, i.e., $$\sum_{\sigma\in S_n}q^{stat(\sigma)} = \sum_{\sigma\in S_n} q^{maj(\sigma )} …

Euler-Mahonian statistics on permutations: A pair of statistic $stat_1,stat_2$ is Euler-Mahonian if it is equidistributed with the bistatistic given by the number of descents and the major index, i.e …

Symmetric statistics on permutations: (maj,inv), (des,dez), (number of crossings, number of nestings) (maximal cardinality of a crossing, maximal cardinality of a nesting)

Symmetric statistics on Dyck paths: The following statistics have a symmetric joint distribution on Dyck paths: (area,bounce), see here (area,dinv), see here (number of returns, length of last desc …

This is more of an expansion of Sam's comments, but too long for a comment itself: As pointed out by Sam in that Theorem 4.2.2.2, tilting modules of the linear type $A_n$ quiver are in natural corres …

Let $E_n(z)$ be the Eulerian polynomial $$E_n(z) = \sum_{\tau \in \mathfrak{S}_n} z^{\operatorname{des}(\tau)}$$ where $\mathfrak{S}_n$ denotes the set of all permutations of $\{1,\ldots,n\}$ and $\op …

For future references: as we have discussed in this question, this also follows from the "zeta map" sending the bistatistic (area,bounce) to the bistatistic (dinv,area). For another definition and fur …