Related papers: Root Cross Z-Complementary Pairs with Large ZCZ Wi…
Non-overlapping codes are a set of codewords in $\bigcup_{n \ge 2} \mathbb{Z}_q^n$, where $\mathbb{Z}_q = \{0,1,\dots,q-1\}$, such that, the prefix of each codeword is not a suffix of any codeword in the set, including itself; and for…
Approximating the roots of a holomorphic function in an input box is a fundamental problem in many domains. Most algorithms in the literature for solving this problem are conditional, i.e., they make some simplifying assumptions, such as,…
An ordered biclique partition of the complete graph $K_n$ on $n$ vertices is a collection of bicliques (i.e., complete bipartite graphs) such that (i) every edge of $K_n$ is covered by at least one and at most two bicliques in the…
We present a bijection between non-crossing partitions of the set $[2n+1]$ into $n+1$ blocks such that no block contains two consecutive integers, and the set of sequences $\{s_{i}\}_{1}^{n}$ such that $1 \leq s_{i} \leq i$, and if…
Due to the increased availability of large datasets of biological sequences, the tools for sequence comparison are now relying on efficient alignment-free approaches to a greater extent. Most of the alignment-free approaches require the…
Let $p\neq3$ be any prime and $l\neq3$ be any odd prime with $gcd(p,l)=1$. $F_{q}^{*}=\langle\xi\rangle$ is decomposed into mutually disjoint union of $gcd(q-1,3lp^{s})$ coset over the subgroup $\langle\xi^{3lp^{s}}\rangle$, where $\xi$ is…
Inspired by Gansner's elegant $k$-trace generating function for rectangular plane partitions, we introduce two novel operators, $\varphi_{z}$ and $\psi_{z}$, along with their combinatorial interpretations. Through these operators, we derive…
In this paper, we compute the number of z-classes (conjugacy classes of centralizers of elements) in the symmetric group S_n, when n is greater or equal to 3 and alternating group A_n, when n is greater or equal to 4. It turns out that the…
There is a well-studied correspondence by Jaclyn Anderson between partitions that avoid hooks of length s or t and certain binary strings of length s+t. Using this map, we prove that the total size of a random partition of this kind…
Quasi-complementary sequence sets (QCSSs) have attracted sustained research interests for simultaneously supporting more active users in multi-carrier code-division multiple-access (MC-CDMA) systems compared to complete complementary codes…
We put recent results on the symmetry of the joint distribution of the numbers of crossings and nestings of two edges over matchings, set partitions and linked partitions, in the larger context of the enumeration of increasing and…
There are many different algebraic, geometric and combinatorial objects that one can attach to a complex polynomial with distinct roots. In this article we introduce a new object that encodes many of the existing objects that have…
This paper introduces the concept of generalized interlacing families of polynomials, which extends the classical interlacing polynomial method to handle polynomials of varying degrees. We establish a fundamental property for these…
We provide a simple proof for a complementary pair of group codes over a finite non-commutative Frobenius ring of the fact that one of them is equivalent to the other one. We also explore this fact for checkeable codes over the same type of…
A graph is an instrument which is extensively utilized to model various problems in different fields. Up to date, many graphs have been developed to represent algebraic structures, particularly rings in order to study their properties. In…
For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array…
In this paper we study pairs of polynomials with a given factorization pattern and such that the degree of their difference attains its minimum. We call such pairs of polynomials Davenport--Zannier pairs, or DZ-pairs for short. The paper is…
In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been…
We solve crossing equations analytically in the deep Euclidean regime. Large scaling dimension $\Delta$ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the…
A collection of families $(\mathcal{F}_{1}, \mathcal{F}_{2} , \cdots , \mathcal{F}_{k}) \in \mathcal{P}([n])^k$ is cross-Sperner if there is no pair $i \not= j$ for which some $F_i \in \mathcal{F}_i$ is comparable to some $F_j \in…