منابع مشابه
Reductions of Young Tableau Bijections
We introduce notions of linear reduction and linear equivalence of bijections for the purposes of study bijections between Young tableaux. Originating in Theoretical Computer Science, these notions allow us to give a unified view of a number of classical bijections, and establish formal connections between them.
متن کاملWhat Is a Young Tableau?
Young tableaux are ubiquitous combinatorial objects making important and inspiring appearances in representation theory, geometry and algebra. They naturally arise in the study of symmetric functions, representation theory of the symmetric and complex general linear groups, and Schubert calculus of Grassmannians. Discovering and interpreting enumerative formulas for Young tableaux (and their ge...
متن کاملBijections between Pattern-avoiding Binary Fillings of Young Diagrams
Pattern-avoiding binary fillings of Young diagrams were first defined and studied by A. Postnikov. Important examples are Γ -diagrams, that are related to decorated permutations and positive Grassman cells. Other examples are acyclic orientations of a graph defined from the Young diagram. Using reccurence relations, he could prove that the numbers of such fillings are equal, for these two examp...
متن کاملOn Selecting a Random Shifted Young Tableau
The study of standard and generalized Young tableaux has led to interesting results in quite a number of areas of mathematics. These arrays are of importance in the representation theory of the symmetric and general linear groups [12], in invariant theory [7], and in connection with various combinatorial problems [ 11. In addition, many algorithms have been developed that manipulate the tableau...
متن کاملBijections between pattern-avoiding fillings of Young diagrams
The pattern-avoiding fillings of Young diagrams we study arose from Postnikov’s work on positive Grassman cells. They are called Γ -diagrams, and are in bijection with decorated permutations. Other closely-related diagrams are interpreted as acyclic orientations of some bipartite graphs. The definition of the diagrams is the same but the avoided patterns are different. We give here bijections p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2010
ISSN: 0895-4801,1095-7146
DOI: 10.1137/070689784