All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 34 Next

Displaying 661 – 680 of 852

Showing per page

Reprezentovatelnost částek ve dvoumincových systémech

Jan Hamáček (2017)

Pokroky matematiky, fyziky a astronomie

Máme-li neomezené množství mincí o předepsaných hodnotách, může se stát, že pomocí nich nelze složit některé částky. Pro jednoduchost se omezíme na případ, kdy máme k dispozici mince pouze dvou různých hodnot. V takovém případě je totiž možné poměrně snadno odvodit vzorce pro největší nereprezentovatelnou částku a zjistit počet všech takových částek. Ukážeme, jak lze ke stejnému cíli dospět různými postupy: nejprve odvodíme vzorec pro zjištění počtu všech nereprezentovatelných částek za pomoci rovinné...

Restricted partitions and q-Pell numbers

Toufik Mansour, Mark Shattuck (2011)

Open Mathematics

In this paper, we provide new combinatorial interpretations for the Pell numbers p n in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by p n. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization of p...

Sagbi bases of Cox–Nagata rings

Bernd Sturmfels, Zhiqiang Xu (2010)

Journal of the European Mathematical Society

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 n -space at n + 3 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....

Secant tree calculus

Dominique Foata, Guo-Niu Han (2014)

Open Mathematics

A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.

Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system

Andrzej Chydziński, Bogdan Smołka (2001)

Applicationes Mathematicae

This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for N=1 through 13 (N is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant....

Currently displaying 661 – 680 of 852