6 citations · 11 across the 22 of their papers we have counts for
25 papers
Consecutive Pattern Containment and c-Wilf Equivalence
Reza Rastegar
We offer elementary proofs for several results in consecutive pattern containment that were previously demonstrated using ideas from cluster method and analytical combinatorics. Fu…
Assorted inequalities for pattern occurrences
Reza Rastegar
In this note, we present several inequalities in the context of pattern containment, utilizing elementary applications of the Fortuin-Kasteleyn-Ginibre (FKG) inequality and Shearer…
On a characterization of exponential and double exponential distributions
Reza Rastegar, Alex Roitershtein
Recently, G.~Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note…
Subregularity in infinitely labeled generating trees of restricted permutations
Toufik Mansour, Reza Rastegar, Mark Shattuck
In this paper, we revisit the application of generating trees to the pattern avoidance problem for permutations. In particular, we study this problem for certain general sets of pa…
Pattern occurrences in -ary words revisited: a few new and old observations
Toufik Mansour, Reza Rastegar
In this paper, we study the pattern occurrence in -ary words. We prove an explicit upper bound on the number of -ary words avoiding any given pattern using a random walk argu…
On column-convex and convex Carlitz polyominoes
Mansour Toufik, Reza Rastegar, Armend Shabani
In this paper, we introduce and study {\it Carlitz polyominoes}. In particular, we show that, as grows to infinity, asymptotically the number of \begin{enumerate} \item column-…
Fixed points of a random restricted growth sequence
Toufik Mansour, Reza Rastegar
We call a fixed point of a given sequence if the value of that sequence at the -th position coincides with . Here, we enumerate fixed points in the class of restricted gr…
Enumeration of Various Animals on the Triangular Lattice
Reza Rastegar, Toufik Mansour
In this paper, we consider various classes of polyiamonds that are animals residing on the triangular lattice. By careful analyses through certain layer-by-layer decompositions and…
Convex polyominoes revisited: Enumeration of outer site perimeter, interior vertices, and boundary vertices of certain degrees
Toufik Mansour, Reza Rastegar
The main contribution of this paper is a new column-by-column method for the decomposition of generating functions of convex polyominoes suitable for enumeration with respect to va…
The longest increasing subsequence in involutions avoiding 3412 and another pattern
Toufik Mansour, Reza Rastegar, Alexander Roitershtein +1
In this note, we study the mean length of the longest increasing subsequence of a uniformly sampled involution that avoids the pattern and another pattern.
On typical triangulations of a convex -gon
Toufik Mansour, Reza Rastegar
Let be a function assigning weight to each possible triangle whose vertices are chosen from vertices of a convex polygon of sides. Suppose is a ran…
Horizontal visibility graph of a random restricted growth sequence
Toufik Mansour, Reza Rastegar, Alexander Roitershtein
We study the distributional properties of horizontal visibility graphs associated with random restrictive growth sequences and random set partitions of size Our main results a…
Extinction scenarios in evolutionary processes: A Multinomial Wright-Fisher approach
Alexander Roitershtein, Reza Rastegar, Robert S. Chapkin +1
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference eq…
Staircase patterns in words: subsequences, subwords, and separation number
Toufik Mansour, Reza Rastegar, Alexander Roitershtein
We revisit staircases for words and prove several exact as well as asymptotic results for longest left-most staircase subsequences and subwords and staircase separation number, the…
Height of records in partitions of a set
Toufik Mansour, Reza Rastegar, Alexander Roitershtein
We study the restricted growth function associated with set partitions, and obtain exact formulas for the number of strong records with height one, the total of record heights over…
Finite automata, probabilistic method, and occurrence enumeration of a pattern in words and permutations
Toufik Mansour, Reza Rastegar, Alexander Roitershtein
The main theme of this paper is the enumeration of the occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence the…
Avalanches in an excitable network
Reza Rastegar, Alexander Roitershtein
We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [23], and is mathematically equivalent to an endemic vari…
On ballistic deposition process on a strip
Toufik Mansour, Reza Rastegar, Alexander Roitershtein
We revisit the model of the ballistic deposition studied in \cite{bdeposition} and prove several combinatorial properties of the random tree structure formed by the underlying stoc…
Random walk on the Poincaré disk induced by a group of Möbius transformations
Charles McCarthy, Gavin Nop, Reza Rastegar +1
We consider a discrete-time random motion, Markov chain on the Poincaré disk. In the basic variant of the model a particle moves along certain circular arcs within the disk, its lo…
Maximum occupation time of a transient excited random walk on Z
Reza Rastegar, Alexander Roitershtein
We consider a transient excited random walk on and study the asymptotic behavior of the occupation time of a currently most visited site. In particular, our results imply that,…
Multivariate linear recursions with Markov-dependent coefficients
D. Hay, R. Rastegar, A. Roitershtein
We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivari…
A High Dynamic Range 3-Moduli-Set with Efficient Reverse Converter
Arash Hariri, K. Navi, Reza Rastegar
-Residue Number System (RNS) is a valuable tool for fast and parallel arithmetic. It has a wide application in digital signal processing, fault tolerant systems, etc. In this work,…
A Step Forward in Studying the Compact Genetic Algorithm
Reza Rastegar, Arash Hariri
The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent popu…
On the Optimal Convergence Probability of Univariate Estimation of Distribution Algorithms
Reza Rastegar
In this paper, we obtain bounds on the probability of convergence to the optimal solution for the compact Genetic Algorithm (cGA) and the Population Based Incremental Learning (PBI…