Related papers: A q-weighted version of the Robinson-Schensted alg…
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…
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 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 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 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 $q$…
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 [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 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 prove a new tableaux formula for the symmetric Macdonald polynomials $P_{\lambda}(X;q,t)$ that has considerably fewer terms and simpler weights than previously existing formulas. Our formula is a sum over certain sorted non-attacking…
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…
A randomisation of the Berele insertion algorithm is proposed, where the insertion of a letter to a symplectic Young tableau leads to a distribution over the set of symplectic Young tableaux. Berele's algorithm provides a bijection between…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
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…
Multiline queues are versatile combinatorial objects that play a key role in understanding the remarkable connection between the asymmetric simple exclusion process (ASEP) on a circle and Macdonald polynomials. Specializing the results of…
In this paper we prove a new combinatorial formula for the modified Macdonald polynomials $\widetilde{H}_\lambda(X;q,t)$, motivated by connections to the theory of interacting particle systems from statistical mechanics. The formula…
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…
We show that the quantum straightening algorithm for Young tableaux and Young bitableaux reduces in the crystal limit $q \mapsto 0$ to the Robinson-Schensted algorithm.
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,…
The optimistic nature of the Q-learning target leads to an overestimation bias, which is an inherent problem associated with standard $Q-$learning. Such a bias fails to account for the possibility of low returns, particularly in risky…