scholarly journals Equidistributed Statistics on Fishburn Matrices and Permutations

10.37236/7926 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Dandan Chen ◽  
Sherry H.F. Yan ◽  
Robin D.P. Zhou
Keyword(s):  
Restricted Permutations

Recently, Jelinek conjectured that there exists a bijection between certain restricted permutations and Fishburn matrices such that the bijection verifies the equidistribution of several statistics. The main objective of this paper is to establish such a bijection.

scholarly journals On the number of certain types of strongly restricted permutations

2010 ◽  
Vol 4 (1) ◽  
pp. 119-135 ◽  
Author(s):  
Vladimir Baltic
Keyword(s):  
Natural Numbers ◽  
Restricted Permutations ◽  
Step Number

Let p be a permutation of the set Nn={1, 2,...,n}. We introduce techniques for counting N(n; k, r, I), the number of Lehmer?s strongly restricted permutations of Nn satisfying the conditions ?k ? p(i)?i ? r (for arbitrary natural numbers k and r) and p(i) ? i I (for some set I). We show that N(n; 1, r, ?) is the Fibonacci (r + 1)-step number.

scholarly journals A Probabilistic Approach to the Asymptotics of the Length of the Longest Alternating Subsequence

10.37236/440 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Christian Houdré ◽  
Ricardo Restrepo
Keyword(s):  
Probabilistic Approach ◽  
Random Permutation ◽  
Probabilistic Methods ◽  
Finite Alphabet ◽  
Restricted Permutations ◽  
Mean Variance

Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a uniform random permutation $\tau\in\left[ n\right] $. Classical probabilistic arguments are used to rederive the asymptotic mean, variance and limiting law of $LA_{n}\left( \tau\right) $. Our methodology is robust enough to tackle similar problems for finite alphabet random words or even Markovian sequences in which case our results are mainly original. A sketch of how some cases of pattern restricted permutations can also be tackled with probabilistic methods is finally presented.

scholarly journals A Generalization of Simion-Schmidt's Bijection for Restricted Permutations

10.37236/1686 ◽  
2003 ◽  
Vol 9 (2) ◽  
Author(s):  
Astrid Reifegerste
Keyword(s):  
Symmetric Group ◽  
Permutation Statistics ◽  
Restricted Permutations ◽  
One To One ◽  
Special Case

We consider the two permutation statistics which count the distinct pairs obtained from the final two terms of occurrences of patterns $\tau_1\cdots\tau_{m-2}m(m-1)$ and $\tau_1\cdots\tau_{m-2}(m-1)m$ in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution over the symmetric group. As a special case we derive a one-to-one correspondence between permutations which avoid each of the patterns $\tau_1\cdots\tau_{m-2}m(m-1)\in{\cal S}_m$ and those which avoid each of the patterns $\tau_1\cdots\tau_{m-2}(m-1)m\in{\cal S}_m$. For $m=3$ this correspondence coincides with the bijection given by Simion and Schmidt in [Europ. J. Combin. 6 (1985), 383-406].

scholarly journals Applications of the finite state automata for counting restricted permutations and variations

2012 ◽  
Vol 22 (2) ◽  
pp. 183-198
Author(s):  
Vladimir Baltic
Keyword(s):  
The Other ◽  
Finite State Automaton ◽  
Finite State Automata ◽  
Combinatorial Structures ◽  
Restricted Permutations ◽  
Finite State

In this paper, we use the finite state automata to count the number of restricted permutations and the number of restricted variations. For each type of restricted permutations, we construct a finite state automaton able to recognize and enumerate them. We, also, discuss how it encompasses the other known methods for enumerating permutations with restricted position, and in one case, we establish connections with some other combinatorial structures, such as subsets and compositions.

scholarly journals Dyck paths and restricted permutations

2006 ◽  
Vol 154 (11) ◽  
pp. 1593-1605 ◽  
Author(s):  
Toufik Mansour ◽  
Eva Y.P. Deng ◽  
Rosena R.X. Du
Keyword(s):  
Restricted Permutations ◽  
Dyck Paths

scholarly journals Refined Restricted Permutations

2002 ◽  
Vol 6 (3) ◽  
pp. 427-444 ◽  
Author(s):  
Aaron Robertson ◽  
Dan Saracino ◽  
Doron Zeilberger
Keyword(s):  
Restricted Permutations

scholarly journals Restricted Permutations

1985 ◽  
Vol 6 (4) ◽  
pp. 383-406 ◽  
Author(s):  
Rodica Simion ◽  
Frank W. Schmidt
Keyword(s):  
Restricted Permutations

scholarly journals Strongly restricted permutations and tiling with fences

2015 ◽  
Vol 187 ◽  
pp. 82-90
Author(s):  
Kenneth Edwards ◽  
Michael A. Allen
Keyword(s):  
Restricted Permutations
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