Related papers: On the combinatorics of tableaux -- Graphical repr…
We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer…
The celebrated Robinson-Schensted algorithm and each of its variants that have attracted substantial attention can be constructed using Fomin's "growth diagram" construction from a modular lattice that is also a weighted-differential poset.…
The two tableaux assigned by the Robinson--Schensted correspondence are equal if and only if the input permutation is an involution, so the RS algorithm restricts to a bijection between involutions in the symmetric group and standard…
Schensted row insertion is a fundamental component of the Robinson-Schensted-Knuth (RSK) algorithm, a powerful tool in combinatorics and representation theory. This study examines the insertion of a deterministic number into a random…
In O'Connell-Pei(2013) a q-weighted version of the Robinson-Schensted algorithm was introduced. In this paper we show that this algorithm has a symmetry property analogous to the well known symmetry property of the normal Robinson-Schensted…
The numbers $f_\lambda$ of standard tableaux of shape $\lambda\vdash n$ satisfy 2 fundamental recursions: $f_\lambda = \sum f_{\lambda^-}$ and $(n + 1)f_\lambda=\sum f_{\lambda^+}$, where $\lambda^-$ and $\lambda^+$ run over all shapes…
In this work, we introduce new combinatorial objects called Dyck tableaux, which present a natural insertion algorithm. These tools may be useful to describe statistics which are relevant in the study of the physical model named PASEP.
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
We give an extension of the classical Schensted correspondence to the case of ribbon tableaux, where ribbons are allowed to be of different sizes. This is done by extending Fomin's growth diagram approach of the classical correspondence…
We introduce a q-weighted version of the Robinson-Schensted (column insertion) algorithm which is closely connected to q-Whittaker functions (or Macdonald polynomials with t=0) and reduces to the usual Robinson-Schensted algorithm when q=0.…
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layout algorithm is required to determine the optimal rendering…
The Little map and the Edelman-Greene insertion algorithm, a generalization of the Robinson-Schensted correspondence, are both used for enumerating the reduced decompositions of an element of the symmetric group. We show the Little map…
I will present a way to implement graph algorithms which is different from traditional methods. This work was motivated by the belief that some ideas from software engineering should be applied to graph algorithms. Re-usability of software…
We describe a relationship between Robinson-Schensted algorithms defined for standard domino tableaux of unequal rank. The principal idea is the moving-through operation defined on standard domino tableaux by D. Garfinkle. When restricted…
Fomin (1994) introduced a notion of duality between two graded graphs on the same set of vertices. He also introduced a generalization to dual graded graphs of the classical Robinson-Schensted-Knuth algorithm. We show how Fomin's approach…
An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…
Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…