Related papers: Pinnacle sets revisited

For the tensor of coherences parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at infinitesimal level. The main advantage of this formalism (clearly reminiscent of the…

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…

Let $A(\ell,n,k)$ denote the number of $\ell$-tuples of commuting permutations of $n$ elements whose permutation action results in exactly $k$ orbits or connected components. We provide a new proof of an explicit formula for $A(\ell,n,k)$…

The tensor product of two differential forms of degree $p$ and $q$ is a multilinear form that is alternating in its first $p$ arguments and alternating in its last $q$ arguments. These forms, which are known as double forms or…

Let $\spt(n)$ be the number of smallest parts in the partitions of $n$. In this paper, we give some generalized Euler-like recursive formulas for the $\spt$ function in terms of Hecke trace of values of special twisted quadratic Dirichlet…

We propose and develop a new method to classify orbits of the spin group ${\rm Spin}(2d)$ in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents, imposing the…

Let $s$ be West's deterministic stack-sorting map. A well-known result (West) is that any length $n$ permutation can be sorted with $n-1$ iterations of $s.$ In 2020, Defant introduced the notion of highly-sorted permutations -- permutations…

Let n be a positive integer greater than or equal to 2, and q a complex number, transcendental over Q. In this paper, we give an algorithmic construction of an ordered bijection between the set of H-primes of n \times n quantum matrices and…

Motivated by recent work of Hanser and Mayers, we study two combinatorial puzzles arising from the theory of Kohnert polynomials. Such polynomials are defined as generating polynomials for certain collections of diagrams consisting of unit…

We construct four new classes of permutation trinomials over the cubic extension of a finite field with even characteristic. Additionally, we explicitly provide the compositional inverse of each class of permutation trinomials in polynomial…

Let $\mathcal{R}$ be a unital ring with involution. The notions of 1MP-inverse and MP1-inverse are extended from $M_{m,n}(\mathbb{C)}$, the set of all $m\times n $ matrices over $\mathbb{C}$, to the set $\mathcal{R}% ^{\dagger}$ of all…

We find all $P$-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces Jan Steven's list [Manuscripta Math. 1993] of the numbers…

In this paper we discuss a new way to derive neutrino mixing patterns, which originates from the idea proposed in a recent article by Hernandez and Smirnov. Its applications to various cases are discussed. We first present the complete set…

Consider a permutation $\sigma\in S_n$ as a deck of cards numbered from 1 to $n$ and laid out in a row, where $\sigma_j$ denotes the number of the card that is in the $j$-th position from the left.\rm\ We study some probabilistic and…

This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…

We investigate the structure and reconstruction complexity of Manacher arrays. First, we establish a combinatorial lower bound, proving that the number of rooted tandem repeat trees with $n+1$ genes exceeds the number of distinct Manacher…

Denote by $\mathbb{N}$ and $\mathbb{P}$ the set of all positive integers and prime numbers, respectively. Let $\mathbb{P}=\{p_1<p_2<\dots <p_n<\dots\}$, where $p_n$ is the $n$-th prime number. For $k\in\mathbb{N}$ we recursively define…

Our main theorems provide a single geometric setting in which polynomial representatives for Schubert classes in the integral cohomology ring of the flag manifold are determined uniquely, and have positive coefficients for geometric…

The observation of light super-partners from a supersymmetric extension to the Standard Model is an intensely sought-after experimental outcome, providing an explanation for the stabilization of the electroweak scale and indicating the…