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$h^{*}$ -vectors, Eulerian polynomials and stable polytopes of graphs.

Athanasiadis, Christos A. (2004)

The Electronic Journal of Combinatorics [electronic only]

Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property.

Bonato, Anthony, Holzmann, W.H., Kharaghani, Hadi (2001)

The Electronic Journal of Combinatorics [electronic only]

Hall-Littlewood functions and Kostka-Foulkes polynomials in representation theory.

Désarménien, J., Leclerc, B., Thibon, J.-Y. (1994)

Séminaire Lotharingien de Combinatoire [electronic only]

Hardness of embedding simplicial complexes in $ℝ^{d}$

Jiří Matoušek, Martin Tancer, Uli Wagner (2011)

Journal of the European Mathematical Society

Let ${𝙴𝙼𝙱𝙴𝙳}_{k \to d}$ be the following algorithmic problem: Given a ﬁnite simplicial complex $K$ of dimension at most $k$ , does there exist a (piecewise linear) embedding of $K$ into $ℝ^{d}$ ? Known results easily imply polynomiality of ${𝙴𝙼𝙱𝙴𝙳}_{k \to 2}$ ( $k = 1, 2$ ; the case $k = 1, d = 2$ is graph planarity) and of ${𝙴𝙼𝙱𝙴𝙳}_{k \to 2 k}$ for all $k \geq 3$ . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that ${𝙴𝙼𝙱𝙴𝙳}_{d \to d}$ and ${𝙴𝙼𝙱𝙴𝙳}_{(d - 1) \to d}$ are undecidable for each $_{d} \geq 5$ . Our main result is NP-hardness of ${𝙴𝙼𝙱𝙴𝙳}_{2 \to 4}$ and, more generally, of ${𝙴𝙼𝙱𝙴𝙳}_{k \to d}$ for all $k$ , $d$ with...

Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Pavel Etingof, Wee Liang Gan, Victor Ginzburg, Alexei Oblomkov (2007)

Publications Mathématiques de l'IHÉS

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...

Harmonic functions on multiplicative graphs and interpolation polynomials.

Borodin, Alexei, Olshanski, Grigori (2000)

The Electronic Journal of Combinatorics [electronic only]

Higher-dimensional cluster combinatorics and representation theory

Steffen Oppermann, Hugh Thomas (2012)

Journal of the European Mathematical Society

Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite-dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied. Cyclic polytopes are classical objects of study in convex geometry. In particular, their triangulations have been studied with a view towards generalizing the rich combinatorial structure of triangulations of polygons. In this paper, we demonstrate a connection...

Hoeffding spaces and Specht modules

Giovanni Peccati, Jean-Renaud Pycke (2011)

ESAIM: Probability and Statistics

It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

Hoeffding spaces and Specht modules

Giovanni Peccati, Jean-Renaud Pycke (2011)

ESAIM: Probability and Statistics

Homogeneous representations of Khovanov–Lauda Algebras

Alexander Kleshchev, Arun Ram (2010)

Journal of the European Mathematical Society

We construct irreducible graded representations of simply laced Khovanov–Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson–Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.

Hook length formula and geometric combinatorics.

Pak, Igor (2001)

Séminaire Lotharingien de Combinatoire [electronic only]

Hook lengths in a skew Young diagram.

Janson, Svante (1997)

The Electronic Journal of Combinatorics [electronic only]

Hopf algebras and dendriform structures arising from parking functions

Jean-Christophe Novelli, Jean-Yves Thibon (2007)

Fundamenta Mathematicae

We introduce a graded Hopf algebra based on the set of parking functions (hence of dimension ${(n + 1)}^{n - 1}$ in degree n). This algebra can be embedded into a noncommutative polynomial algebra in infinitely many variables. We determine its structure, and show that it admits natural quotients and subalgebras whose graded components have dimensions respectively given by the Schröder numbers (plane trees), the Catalan numbers, and powers of 3. These smaller algebras are always bialgebras and belong to some family...

Hyperoctahedral species.

Bergeron, N., Choquette, P. (2009)

Séminaire Lotharingien de Combinatoire [electronic only]

Hypersymmetric functions and Pochhammers of $2 \times 2$ nonautonomous matrices.

Antippa, A.F. (2004)

International Journal of Mathematics and Mathematical Sciences

Currently displaying 1 – 15 of 15

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