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On montre que les composantes irréductibles du lieu singulier d’une variété de Schubert dans $G L_{n} / B,$ associée à une permutation covexillaire, sont paramétrées par certains des points coessentiels du graphe de la permutation. On donne une description explicite de ces composantes et l’on décrit la singularité le long de chacune d’entre elles.

Six little squares and how their numbers grow.

Beck, Matthias, Zaslavsky, Thomas (2010)

Journal of Integer Sequences [electronic only]

Size of the giant component in a random geometric graph

Ghurumuruhan Ganesan (2013)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we study the size of the giant component $C_{G}$ in the random geometric graph $G = G (n, r_{n}, f)$ of $n$ nodes independently distributed each according to a certain density $f (\cdot)$ in ${[0, 1]}^{2}$ satisfying ${inf}_{x \in {[0, 1]}^{2}} f (x) g t;$ $0$ . If $\frac{c_{1}}{n} \leq r_{n}^{2} \leq c_{2} \frac{log n}{n}$ for some positive constants $c_{1}$ , $c_{2}$ and $n r_{n}^{2} ⟶ \infty$ as $n \to \infty$ , we show that the giant component of $G$ contains at least $n - o (n)$ nodes with probability at least $1 - e^{- β n r_{n}^{2}}$ for all $n$ and for some positive constant $β$ ....

Skein algebras of the solid torus and symmetric spatial graphs

Nafaa Chbili (2006)

Fundamenta Mathematicae

We use the topological invariant of spatial graphs introduced by S. Yamada to find necessary conditions for a spatial graph to be periodic with a prime period. The proof of the main result is based on computing the Yamada skein algebra of the solid torus and then proving that it injects into the Kauffman bracket skein algebra of the solid torus.

Skeletons in multigraphs

Václav Havel, Josef Klouda (1993)

Commentationes Mathematicae Universitatis Carolinae

Under a multigraph it is meant in this paper a general incidence structure with finitely many points and blocks such that there are at least two blocks through any point and also at least two points on any block. Using submultigraphs with saturated points there are defined generating point sets, point bases and point skeletons. The main result is that the complement to any basis (skeleton) is a skeleton (basis).

Skew divided difference operators and Schubert polynomials.

Kirillov, Anatol N. (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Skew spectra of oriented graphs.

Shader, Bryan, So, Wasin (2009)

The Electronic Journal of Combinatorics [electronic only]

Skew-symmetric cluster algebras of finite mutation type

Anna Felikson, Michael Shapiro, Pavel Tumarkin (2012)

Journal of the European Mathematical Society

In the famous paper [FZ2] Fomin and Zelevinsky obtained Cartan-Killing type classification of all cluster algebras of finite type, i.e. cluster algebras having only finitely many distinct cluster variables. A wider class of cluster algebras is formed by cluster algebras of finite mutation type which have finitely many exchange matrices (but are allowed to have infinitely many cluster variables). In this paper we classify all cluster algebras of finite mutation type with skew-symmetric exchange matrices....

Sklyanin determinant for reflection algebra.

Rozhkovskaya, Natasha (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Skolem-type difference sets for cycle systems.

Bryant, Darryn, Gavlas, Heather, Ling, Alan C.H. (2003)

The Electronic Journal of Combinatorics [electronic only]

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