Br\"{a} nd\'{e} n and Claesson introduced the concept of mesh patterns in 2011, and since
then, these patterns have attracted significant attention in the literature. Subsequently, in …

The Parks Puzzle is a paper-and-pencil puzzle game that is classically played on a square
grid with different colored regions (the parks). The player needs to place a certain number …

Dold sequences constitute an important class of integer sequences that play an important
role in combinatorics, number theory, topology and dynamical systems. We generalize the …

A digit $\pi_j $ in a permutation $\pi=[\pi_1,\ldots,\pi_n]\in S_n $ is defined to be a separator
of $\pi $ if by omitting it from $\pi $ we get a new $2-$ block. In this work we introduce a new …

Sn. Thus, to characterize the sparseness of the downset of a permutation σ∈ Sn, we aim not
only to find the number of bonds in σ, but also to predict the number of bonds contained in its …

We call a permutation $\sigma=[\sigma_1,\dots,\sigma_n]\in S_n $ a {\em cylindrical king
permutation} if $|\sigma_i-\sigma_ {i+ 1}|> 1$ for each $1\leq i\leq n-1$ and $|\sigma_1 …

We present a new variant of the secretary problem. Let $ A $ be a totally ordered set of $ n
$\emph {applicants}. Given $ P\subseteq A $ and $ x\in A $, let $ rr (P, x)=\vert\{z\in P\mid …

Let Sn be the Symmetric group of n elements. A 2− block or a bond in a permutation
π=[π1,..., πn]∈ Sn is a consecutive sub-sequence of π of the form πi, πi+1 such that| πi …