scholarly journals Unimodality of partitions in near-rectangular Ferrers diagrams

2015 ◽  
Vol 338 (9) ◽  
pp. 1649-1658
Author(s):  
Samuel Zbarsky
Keyword(s):  
Ferrers Diagrams

scholarly journals Tree-like tableaux

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Jean-Christophe Aval ◽  
Adrien Boussicault ◽  
Philippe Nadeau
Keyword(s):  
Insertion Procedure ◽  
International Audience ◽  
Ferrers Diagrams

International audience 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 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. Dans ce travail nous introduisons et étudions les tableaux boisés, qui sont certains remplissages de diagrammes de Ferrers en bijection simple avec les tableaux de permutation et les tableaux alternatifs. Nous décrivons une procédure d'insertion élémentaire sur nos tableaux qui donne une preuve limpide que les tableaux de taille n sont comptés par n!, et qui de plus respecte la plupart des statistiques standard sur les tableaux de permutation et tableaux alternatifs. Notre procédure d'insertion permet en particulier de définir deux nouvelles bijections simples entre tableaux et permutations: la première est conçue spécifiquement pour respecter le motif généralisé 2-31 sur les permutations, tandis que la deuxième respecte l'arbre binaire sous-jacent à un tableau boisé.

scholarly journals Tree-like Tableaux

10.37236/3440 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Jean-Christophe Aval ◽  
Adrien Boussicault ◽  
Philippe Nadeau
Keyword(s):  
Insertion Procedure ◽  
Ferrers Diagrams

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.

scholarly journals Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks

2015 ◽  
Vol 61 (7) ◽  
pp. 3937-3953 ◽  
Author(s):  
Natalia Silberstein ◽  
Anna-Lena Trautmann
Keyword(s):  
Subspace Codes ◽  
Ferrers Diagrams

scholarly journals Volume Laws for Boxed Plane Partitions and Area Laws for Ferrers Diagrams

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Uwe Schwerdtfeger
Keyword(s):  
Uniform Distribution ◽  
Random Variables ◽  
Symmetry Class ◽  
Limit Laws ◽  
Plane Partitions ◽  
Symmetric Plane ◽  
International Audience ◽  
Ferrers Diagrams ◽  
Area Limit

International audience We asymptotically analyse the volume random variables of general, symmetric and cyclically symmetric plane partitions fitting inside a box. We consider the respective symmetry class equipped with the uniform distribution. We also prove area limit laws for two ensembles of Ferrers diagrams. Most limit laws are Gaussian.

scholarly journals Enumeration of skew Ferrers diagrams

1993 ◽  
Vol 112 (1-3) ◽  
pp. 65-79 ◽  
Author(s):  
M.P. Delest ◽  
J.M. Fedou
Keyword(s):  
Ferrers Diagrams

scholarly journals Visual thinking and simplicity of proof

2019 ◽  
Vol 377 (2140) ◽  
pp. 20180032 ◽  
Author(s):  
Alan J. Cain
Keyword(s):  
Simple Proof ◽  
Spatial Reasoning ◽  
Visual Representations ◽  
Spatial Thinking ◽  
Visual Thinking ◽  
Theme Issue ◽  
Informal Proof ◽  
Ferrers Diagrams ◽  
Partitions Of Integers

This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual representations of partitions of integers) and comparing them to proofs that do not use spatial thinking. The analysis shows that using diagrams and spatial thinking can contribute to simplicity by (for example) avoiding technical calculations, division into cases, and induction, and creating a more surveyable and explanatory proof (both of which are connected to simplicity). In response to one part of Hilbert's 24th problem, the area between two proofs is explored in one example, showing that between a proof that uses spatial reasoning and one that does not, there is a proof that is less simple yet more impure than either. This has implications for the supposed simplicity of impure proofs. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.

scholarly journals Koszul blowup algebras associated to three-dimensional Ferrers diagrams

2018 ◽  
Vol 514 ◽  
pp. 219-253 ◽  
Author(s):  
Kuei-Nuan Lin ◽  
Yi-Huang Shen
Keyword(s):  
Three Dimensional ◽  
Ferrers Diagrams
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