相关论文: Jeu de taquin, uniqueness of rectification, and ul…

This paper presents a combinatorial study of the super plactic monoid of type A, which is related to the representations of the general linear Lie superalgebra. We introduce the analogue of the Sch\"{u}tzenberger's jeu de taquin on the…

Young tableaux are fundamental objects in algebraic combinatorics and representation theory, with operations such as promotion and jeu de taquin playing a central role in their structure and applications. While these operations are well…

An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a…

Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the…

We present a new characterization of the shape equivalent class and the Littlewood-Richardson correspondence of Young tableaux in terms of tropical (ultradiscrete) integrable systems. As an application, an alternative proof of the "shape…

We establish a combinatorial connection between the real geometry and the $K$-theory of complex Schubert curves $S(\lambda_\bullet)$, which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal…

Serrano (2010) introduced the shifted plactic monoid, governing Haiman's (1989) mixed insertion algorithm, as a type B analogue of the classical plactic monoid that connects jeu de taquin of Young tableaux with the Robinson-Schensted-Knuth…

In this paper we further develop the theory of geometric tropicalization due to Hacking, Keel and Tevelev and we describe tropical methods for implicitization of surfaces. More precisely, we enrich this theory with a combinatorial formula…

The jeu-de-taquin-based Littlewood-Richardson rule of H. Thomas and A. Yong (2009) for minuscule varieties has been extended in two orthogonal directions, either enriching the cohomology theory or else expanding the family of varieties…

We establish a combinatorial connection between the real geometry and the $K$-theory of complex Schubert curves $S(\lambda_\bullet)$, which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal…

In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the…

We develop a tropical analog of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m+n)) time, where m…

An algorithm to give an explicit description of all the solutions to any tropical linear system $A\odot x=B\odot x$ is presented. The given system is converted into a finite (rather small) number $p$ of pairs $(S,T)$ of classical linear…

The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin…

In this paper, we show how various combinatorial algorithms of Young tableaux naturally arise from the WKB approximation of the connection matrix of quantum confluent hypergeometric equation, including the Robinson-Schensted algorithm, the…

This paper is about the combinatorics of finite point configurations in the tropical projective space or, dually, of arrangements of finitely many tropical hyperplanes. Moreover, arrangements of finitely many tropical halfspaces can be…

We define and study the Plancherel-Hecke probability measure on Young diagrams; the Hecke algorithm of [Buch-Kresch-Shimozono-Tamvakis-Yong '06] is interpreted as a polynomial-time exact sampling algorithm for this measure. Using the…

We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorial interpretation and proof of the geometric rule…

We study "cominuscule tableau combinatorics" by generalizing constructions of M. Haiman, S. Fomin and M.-P. Sch\"utzenberger. In particular, we extend the dual equivalence ideas of [Haiman, 1992] to reformulate the generalized…

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…