相关论文: Cumulants of threshold for Schensted row insertion…

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…

We investigate the evolution in time of the position of a fixed number in the insertion tableau when the Robinson-Schensted-Knuth algorithm is applied to a sequence of random numbers. When the length of the sequence tends to infinity, a…

We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the $y$-axis) when a specified number is inserted into a large Plancherel-distributed tableau.…

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.…

Many algorithms for inserting elements into tableaux are known, starting with the Robinson-Schensted algorithm. Much of those processes can be incorporated into the general framework of Fomin's "growth diagrams". Even for single types of…

We introduce and study q-randomized Robinson-Schensted-Knuth (RSK) correspondences which interpolate between the classical (q=0) and geometric (q->1) RSK correspondences (the latter ones are sometimes also called tropical). For 0<q<1 our…

We investigate Robinson-Schensted-Knuth algorithm (RSK) and Sch\"utzenberger's jeu de taquin in the infinite setup. We show that the recording tableau in RSK defines an isomorphism of the following two dynamical systems: (i) a sequence of…

The Robinson-Schensted-Knuth (RSK) correspondence is a bijective correspondence between two-rowed arrays of non-negative integers and pairs of same-shape semistandard tableaux. This correspondence satisfies the symmetry property, that is,…

In [Matveev-Petrov 2016](arXiv:1504.00666) a $q$-deformed Robinson-Schensted-Knuth algorithm ($q$RSK) was introduced. In this article we give reformulations of this algorithm in terms of the Noumi-Yamada description, growth diagrams and…

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…

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…

We introduce a probabilistic generalization of the dual Robinson--Schensted--Knuth correspondence, called $qt$RSK${}^*$, depending on two parameters $q$ and $t$. This correspondence extends the $q$RS$t$ correspondence, recently introduced…

We present a probabilistic generalization of the Robinson--Schensted correspondence in which a permutation maps to several different pairs of standard Young tableaux with nonzero probability. The probabilities depend on two parameters $q$…

We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…

We introduce an insertion algorithm on Kohnert's combinatorial model for Demazure characters, generalizing Robinson--Schensted--Knuth insertion on tableaux. Our new insertion yields an explicit, nonnegative formula expressing the product of…

We prove a limit shape theorem describing the asymptotic shape of bumping routes when the Robinson-Schensted algorithm is applied to a finite sequence of independent, identically distributed random variables with the uniform distribution…

We present a probabilistic generalization of the Robinson--Schensted correspondence in which a permutation maps to several different pairs of standard Young tableaux with nonzero probability. The probabilities depend on two parameters $q$…

The Berele row-insertion is a symplectic analogue of the Schensted row-insertion. In the present paper, we provide it with a representation theoretical interpretation via the quantum symmetric pairs of type $A\mathrm{II}$. As applications,…

We introduce an object called a decorated Young tableau which can equivalently be viewed as a continuous time trajectory of Young diagrams or as a non-intersecting line ensemble. By a natural extension of the Robinson-Schensted…

We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at random. We give a formula for the probability of choosing a…