Open AccessPosted Content
Tree-like tableaux
TL;DR: In this article, the authors introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux.
read more
Abstract: In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tree-like tableaux of size n are counted by n!, and which moreover respects most of the well-known statistics studied originally on alternative and permutation tableaux. Our insertion procedure allows to define in particular two simple new bijections between tree-like tableaux and permutations: the first one is conceived specifically to respect the generalized pattern 2-31, while the second one respects the underlying tree of a tree-like tableau.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
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
The On-Line Encyclopedia of Integer Sequences
Neil J. A. Sloane
- 27 Jun 2007
TL;DR: The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
•Posted Content
Total positivity, Grassmannians, and networks
TL;DR: In this article, the authors discuss the relationship between total positivity and planar directed networks and show that the inverse boundary problem for these networks is naturally linked with the study of the totally nonnegative Grassmannian.
782
On Some Properties of Permutation Tableaux
TL;DR: In this paper, the relations between various permutation statistics and properties of permutation tableaux are investigated, in particular on the distribution of the bistatistic of numbers of rows and essential ones in permutation tables.
Total positivity for cominuscule Grassmannians
Thomas Lam,Lauren Williams +1 more
TL;DR: In this paper, the combinatorics of the nonneg-ative part (G/P ) of a cominuscule Grassmannian are explored in terms of pattern avoidance.