On Some Properties of Permutation Tableaux
By Alexander Burstein. 2007
51 citations recorded by the source corpus.
Abstract.We consider the relations between various permutation statistics and properties of permutation tableaux. We answer some of the open problems of Steingrímsson and Williams [8], in particular, on the distribution of the bistatistic of numbers of rows and essential ones in permutation tableaux. We also consider and enumerate sets of permutation tableaux related to some pattern restrictions on permutations.
Subfields: Algebra and Number Theory, Artificial Intelligence, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/8499dc26c2ab81533b870c33e834fcf7efd127ea
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In Algebra and Number Theory
- Lauren K. Williams
- Sylvie Corteel
- Yuji Kodama
- Ralf Schiffler
- Greg Muller
- Alexander Postnikov
- S. Chakravarty
In Artificial Intelligence
In Discrete Mathematics and Combinatorics
- Dennis Stanton
- Richard P. Stanley
- Sylvie Corteel
- Lauren K. Williams
- Michelle L. Wachs
- Petter Brand'en
- Yuji Kodama
- Greg Muller
Citations in the corpus
- Formulae for Askey-Wilson moments and enumeration of staircase tableaux (2010, background): “roduced by Viennot [31]. These bijections are explained in [12, Section 9]. As a consequence, the staircase tableaux of size n with only α’s and β’s are in bijection with permutations on n +1 letters [28, 8, 4]. Moreover, one can interpret the parameter q as counting the number of crossings or the n”
- Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials (2009, background): “Subsequently [10] and [12] observed that a permutation tableau is determined by complementary statistics, namely the positions of the topmost 1’s not in the first row, and rightmost restricted zero’s.”