Zobrazeno 1 - 10
of 144
pro vyhledávání: '"Readdy, Margaret"'
We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung-Feller theorem. Both classes of permutations are counted by the Fuss-Catalan numbers. The study of one class leads to
Externí odkaz:
http://arxiv.org/abs/2310.06288
Let $\mathcal{H}$ be a Coxeter hyperplane arrangement in $n$-dimensional Euclidean space. Assume that the negative of the identity map belongs to the associated Coxeter group $W$. Furthermore assume that the arrangement is not of type $A_1^n$. Let $K
Externí odkaz:
http://arxiv.org/abs/2105.07288
We introduce and prove the $n$-dimensional Pizza Theorem: Let $\mathcal{H}$ be a hyperplane arrangement in $\mathbb{R}^{n}$. If $K$ is a measurable set of finite volume, the {pizza quantity} of $K$ is the alternating sum of the volumes of the regions
Externí odkaz:
http://arxiv.org/abs/2102.06649
This article is concerned with the constants that appear in Harish-Chandra's character formula for stable discrete series of real reductive groups, although it does not require any knowledge about real reductive groups or discrete series. In Harish-C
Externí odkaz:
http://arxiv.org/abs/1912.00506
The full root polytope of type $A$ is the convex hull of all pairwise differences of the standard basis vectors which we represent by forward and backward arrows. We completely classify all flag triangulations of this polytope that are uniform in the
Externí odkaz:
http://arxiv.org/abs/1901.07113
In the computation of the intersection cohomology of Shimura varieties, or of the $L^2$ cohomology of equal rank locally symmetric spaces, combinatorial identities involving averaged discrete series characters of real reductive groups play a large te
Externí odkaz:
http://arxiv.org/abs/1806.09175
Publikováno v:
Electronic Journal of Combinatorics, 25 Issue 1 (2018), Paper #P1.37
We give combinatorial proofs of $q$-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the $q$-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel $q$-Stirling
Externí odkaz:
http://arxiv.org/abs/1706.06623
Publikováno v:
Journal of Integer Sequences, Vol. 19 (2016), Article 16.7.8
We give a new $q$-$(1+q)$-analogue of the Gaussian coefficient, also known as the $q$-binomial which, like the original $q$-binomial $\genfrac{[}{]}{0pt}{}{n}{k}_{q}$, is symmetric in $k$ and $n-k$. We show this $q$-$(1+q)$-binomial is more compact t
Externí odkaz:
http://arxiv.org/abs/1609.03216
We show that Simion's type $B$ associahedron is combinatorially equivalent to a pulling triangulation of a type $B$ root polytope called the Legendre polytope. Furthermore, we show that every pulling triangulation of the Legendre polytope yields a fl
Externí odkaz:
http://arxiv.org/abs/1607.06061
Publikováno v:
J. Number Theory, 172 (2017), 287--300
We introduce the van der Waerden complex ${\rm vdW}(n,k)$ defined as the simplicial complex whose facets correspond to arithmetic progressions of length $k$ in the vertex set $\{1, 2, \ldots, n\}$. We show the van der Waerden complex ${\rm vdW}(n,k)$
Externí odkaz:
http://arxiv.org/abs/1605.00663