scholarly journals On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation

2007 ◽  
Vol 31 (2) ◽  
pp. 227-238 ◽  
Author(s):  
M. H. Albert
Keyword(s):  
Random Permutation ◽  
Longest Subsequence

Asymptotics with remainder term for moments of the total cycle number of random A-permutation

2021 ◽  
Vol 31 (1) ◽  
pp. 51-60
Author(s):  
Arsen L. Yakymiv
Keyword(s):  
Remainder Term ◽  
Random Permutation ◽  
Natural Numbers ◽  
Cycle Number ◽  
Fixed Set ◽  
Cycle Lengths

Abstract Dedicated to the memory of Alexander Ivanovich Pavlov. We consider the set of n-permutations with cycle lengths belonging to some fixed set A of natural numbers (so-called A-permutations). Let random permutation τ n be uniformly distributed on this set. For some class of sets A we find the asymptotics with remainder term for moments of total cycle number of τ n .

scholarly journals DNA Cryptographic System Utilizing Random Permutation

2020 ◽  
Vol 8 (5) ◽  
pp. 4133-4138
Keyword(s):  
Information Security ◽  
Dna Computing ◽  
Research Paper ◽  
Random Permutation ◽  
Dna Bases ◽  
Highly Efficient ◽  
Cryptographic System ◽  
Encryption Decryption

The study of encryption/decryption of information is known as cryptography. The need of protecting information from old years until now is the reason of appearing the process of hiding information from unauthorized people to access it. In this research paper, a cryptographic system is designed by using the DNA computing concepts and random permutation. The proposed system is a block symmetric cipher that uses one initial key in which will be used to generate permutations as many as needed, convert the initial key to DNA key, convert plaintext block to DNA bases. The remaining needed DNA keys are produced through the cipher/deciphering processing. Different operations applied: permute using permutation, modulo and XOR operations to perform the encryption/decryption process. Using the DNA based cryptography enhance the information security and produce highly efficient cipher systems.

scholarly journals Lower Bounds for the Size of Random Maximal $H$-Free Graphs

10.37236/93 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Guy Wolfovitz
Keyword(s):  
Lower Bound ◽  
Random Process ◽  
Lower Bounds ◽  
Random Permutation ◽  
Bipartite Graphs ◽  
Expected Number ◽  
Free Graph ◽  
Vertex Graph

We consider the next random process for generating a maximal $H$-free graph: Given a fixed graph $H$ and an integer $n$, start by taking a uniformly random permutation of the edges of the complete $n$-vertex graph $K_n$. Then, traverse the edges of $K_n$ according to the order imposed by the permutation and add each traversed edge to an (initially empty) evolving $n$-vertex graph - unless its addition creates a copy of $H$. The result of this process is a maximal $H$-free graph ${\Bbb M}_n(H)$. Our main result is a new lower bound on the expected number of edges in ${\Bbb M}_n(H)$, for $H$ that is regular, strictly $2$-balanced. As a corollary, we obtain new lower bounds for Turán numbers of complete, balanced bipartite graphs. Namely, for fixed $r \ge 5$, we show that ex$(n, K_{r,r}) = \Omega(n^{2-2/(r+1)}(\ln\ln n)^{1/(r^2-1)})$. This improves an old lower bound of Erdős and Spencer. Our result relies on giving a non-trivial lower bound on the probability that a given edge is included in ${\Bbb M}_n(H)$, conditioned on the event that the edge is traversed relatively (but not trivially) early during the process.

The Total Length of Short Cycles of a Random Permutation: 10732

2001 ◽  
Vol 108 (3) ◽  
pp. 273
Author(s):  
M. N. Deshpande ◽  
John H. Lindsey II
Keyword(s):  
Random Permutation ◽  
Total Length
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