Related papers: RSK and Quantum Symmetric Functions: A Combinatori…
This paper's aim is to present recent combinatorial considerations on r-Dyck paths, r-Parking functions, and the r-Tamari lattices. Giving a better understanding of the combinatorics of these objects has become important in view of their…
Problem instances of a size suitable for practical applications are not likely to be addressed during the noisy intermediate-scale quantum (NISQ) period with (almost) pure quantum algorithms. Hybrid classical-quantum algorithms have…
We introduce the new combinatorial approach of plethystic type of tableaux, as a method to understand coefficients of Schur functions appearing in plethysms $s_\nu[h_\lambda]$ and $s_{\nu}[e_{\lambda}]$, for any partitions $\lambda$ and…
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…
By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various combinatorial algorithms, including the RSK…
Kostka functions $K^{\pm}_{\lambda, \mu}(t)$ associated to complex reflection groups are a generalization of Kostka polynomials, which are indexed by a pair $\lambda, \mu$ of $r$-partitions and a sign $+, -$. It is expected that there…
We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…
Let $\lambda=(\lambda_1 \geqslant \ldots \geqslant \lambda_k > 0)$. For any $c$ Coxeter element of $\mathfrak{S}_{\lambda_1+k-1}$, we construct a bijection from fillings of $\lambda$ to reverse plane partitions. We recover two previous…
In this work, we present a Gauss-Newton based quantum algorithm (GNQA) for combinatorial optimization problems that, under optimal conditions, rapidly converges towards one of the optimal solutions without being trapped in local minima or…
We establish a fundamental connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions, analogous to the well known relationship between the RSK correspondence and Schur functions. This gives rise to a natural family…
We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with…
This paper provides an exploration of parking functions, a classical combinatorial object. We present two viewpoints on their structure and properties: through poset of noncrossing partitions and polytopes.
Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we introduce and describe the…
Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications…
We present a library of formalized results around symmetric functions and the character theory of symmetric groups. Written in Coq/Rocq and based on the Mathematical Components library, it covers a large part of the contents of a graduate…
Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible transformations. This paper presents new computational…
Kostka, Littlewood-Richardson, Plethysm and Kronecker coefficients are the multiplicities of irreducible representations in the decomposition of representations of the symmetric group that play an important role in representation theory,…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…