Related papers: On Universal Cycles for new Classes of Combinatori…

For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper we…

The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length $n$ and edges that are permutations of length $n+1$ in which an edge $a_1\cdots…

If every element of a matrix group is similar to a permutation matrix, then it is called a permutation-like matrix group. References [4], [5] and [6] showed that, if a permutation-like matrix group contains a maximal cycle such that the…

In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…

Let $k,a,b$ be positive integers with $a+b=k$. A $k$-uniform hypergraph is called an $(a,b)$-cycle if there is a partition $(A_0,B_0,A_1,B_1,\ldots,A_{t-1},B_{t-1})$ of the vertex set with $|A_i|=a$, $|B_i|=b$ such that $A_i\cup B_i$ and…

A cyclic subgroup $N$ of a finite group $G$ is called a uni-width subgroup of $G$ if $N$ is the unique cyclic subgroup of $G$ of order $|N|$. In this article, we prove that a finite group $G$ admits a unique largest uni-width subgroup…

We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences. There exist frequently hypercyclic operators with upper-frequently hypercyclic…

Heffter arrays are combinatorial structures used to construct orthogonal cyclic cycle decompositions and biembeddings of complete graphs onto surfaces. A Heffter array $H(m,n;h,k)$ is an $m \times n$ partially filled array with distinct…

We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper…

We prove the existence of common hypercyclic entire functions for uncountable families of translation type operators. Contrary to our previous work [34], here the parameter which reflects the uncountable family lies on the unit circle. On…

The union of a collection of $n$ sets is generally expressed in terms of a characteristic (indicator) function that contains $2^{n}-1$ terms. In this article, a much simpler expression is found that requires the evaluation of $n$ terms…

The Hamiltonian cycle polynomial can be evaluated to count the number of Hamiltonian cycles in a graph. It can also be viewed as a list of all spanning cycles of length $n$. We adopt the latter perspective and present a pair of original…

Any permutation polynomial is an $ n $-cycle permutation. When $n$ is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These…

We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in $[0,\frac{1}{3}]$, answering a question of Cameron, and that the number of those…

In this paper we generalize permutations to plane permutations. We employ this framework to derive a combinatorial proof of a result of Zagier and Stanley, that enumerates the number of $n$-cycles $\omega$, for which $\omega(12\cdots n)$…

We view ultrametric spaces as two-sorted structures consisting of a set of points and of a linearly ordered set of distances. We call the appropriate notion of embeddings distance-carrying (dc for short). Those are obtained by combining…

The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…

A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] \dots w[i_{k}]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq \lvert w\rvert$. A word $w$ is $k$-subsequence universal over an alphabet $\Sigma$ if every…

Unbounded SubsetSum is a classical textbook problem: given integers $w_1,w_2,\cdots,w_n\in [1,u],~c,u$, we need to find if there exists $m_1,m_2,\cdots,m_n\in \mathbb{N}$ satisfying $c=\sum_{i=1}^n w_im_i$. In its all-target version, $t\in…

We consider the algorithmic problem of generating each subset of $[n]:=\{1,2,\ldots,n\}$ whose size is in some interval $[k,l]$, $0\leq k\leq l\leq n$, exactly once (cyclically) by repeatedly adding or removing a single element, or by…