-циклические орграфы
Šachové úlohy v kombinatorice
Článek pojednává o matematických úlohách souvisejících se šachovnicí a šachovými figurami. Ze šachu však budeme potřebovat pouze pravidla pro pohyb figur po šachovnici. Postupně se zaměřujeme na jezdcovy procházky po obdélníkových šachovnicích a dále na tzv. nezávislost a dominanci figur a vztah mezi nimi na čtvercových šachovnicích. Ukážeme, že některé problémy lze řešit elegantněji, pokud je přeformulujeme v řeči teorie grafů.
Sachs triangulations, generated by dessins d'enfant, and regular maps
Sagbi bases of Cox–Nagata rings
We degenerate Cox–Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev–Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective -space at points, sagbi bases of Cox–Nagata rings establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D’Cruz–Iarrobino and Buczyńska–Wiśniewski....
Salem numbers, Pisot numbers, Mahler measure, and graphs.
Sampling 3-colourings of regular bipartite graphs.
Satisfiability and computing van der Waerden numbers.
Satisfying states of triangulations of a convex -gon.
Saturation numbers for trees.
Saturation numbers of books.
Scale-free percolation
We formulate and study a model for inhomogeneous long-range percolation on . Each vertex is assigned a non-negative weight , where are i.i.d. random variables. Conditionally on the weights, and given two parameters , the edges are independent and the probability that there is an edge between and is given by . The parameter is the percolation parameter, while describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there...
Scaling limit of isoradial dimer models and the case of triangular quadri-tilings
Schälbare Cohen-Macauley-Komplexe und ihre Parametrisierung.
Schauder fixed point theorem in spaces with global nonpositive curvature.
Schubert and Grothendieck: a bidecennial balance. (Schubert et Grothendieck: un bilan bidécennal.)
Schubert functions and the number of reduced words of permutations.
Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces
The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.
Schur complements of matrices with acyclic bipartite graphs.
Schur functions and alternating sums.
Schur functions: Theme and variations.