Open AccessPosted Content
Juggling probabilities
Gregory S. Warrington
- 20 Feb 2003
TL;DR: The act of a person juggling can be viewed as a Markov process if we assume that the juggler throws to random heights and compute the steady state probabilities in terms of the Stirling numbers of the second kind as discussed by the authors.
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Abstract: The act of a person juggling can be viewed as a Markov process if we assume that the juggler throws to random heights I make this association for the simplest reasonable model of random juggling and compute the steady state probabilities in terms of the Stirling numbers of the second kind I also explore several alternate models of juggling
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Citations
Positroid varieties: juggling and geometry
TL;DR: In this paper, it was shown that the intersection of only the cyclic shifts of one Bruhat decomposition has many of the good properties of the Bruhat and Richardson decompositions.
•Posted Content
Positroid varieties I: juggling and geometry
TL;DR: In this article, the authors show that the strata positroid varieties are normal, Cohen-Macaulay, have rational singularities, and are defined as schemes by the vanishing of Plucker coordinates.
79
Enumerating (Multiplex) Juggling Sequences
Steve Butler,Ron Graham +1 more
TL;DR: In this paper, the problem of enumerating periodic σ-juggling sequences of length n for multiplex juggling, where σ is the initial state (or landing schedule) of the balls, was studied.
References
•Book
Enumerative Combinatorics
R P Stanley
- 13 Apr 1997
Abstract: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.
7.8K
Cauchy's Interlace Theorem for Eigenvalues of Hermitian Matrices
TL;DR: The Cauchy interlace theorem states that the eigenvalues of a Hermitian matrix A of order n are interlaced with those of any principal submatrix of ordern − 1.
•Book
The Mathematics of Juggling
Burkard Polster
- 01 Jan 2003
TL;DR: The Mathematics of Juggling as discussed by the authors is a collection of mostly self-contained mathematical essays that introduce the reader to many elegant results and techniques from a wide range of mathematical disciplines such as combinatorics, graph theory, knot theory, mechanics, differential equations, control theory, and robotics.
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