scholarly journals Occurrence graphs of patterns in permutations

2019 ◽  
Vol 12 (6) ◽  
pp. 901-918
Author(s):  
Bjarni Jens Kristinsson ◽  
Henning Ulfarsson
Keyword(s):  
Patterns In Permutations

scholarly journals Equivalence Classes of Permutations Modulo Replacements Between 123 and Two-Integer Patterns

10.37236/3753 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Vahid Fazel-Rezai
Keyword(s):  
Equivalence Classes ◽  
Classical Sense ◽  
New Type ◽  
Patterns In Permutations

We explore a new type of replacement of patterns in permutations, suggested by James Propp, that does not preserve the length of permutations. In particular, we focus on replacements between 123 and a pattern of two integer elements. We apply these replacements in the classical sense; that is, the elements being replaced need not be adjacent in position or value. Given each replacement, the set of all permutations is partitioned into equivalence classes consisting of permutations reachable from one another through a series of bi-directional replacements. We break the eighteen replacements of interest into four categories by the structure of their classes and fully characterize all of their classes.

scholarly journals Generalized descent patterns in permutations and associated Hopf algebras

2011 ◽  
Vol 32 (4) ◽  
pp. 618-627 ◽  
Author(s):  
Jean-Christophe Novelli ◽  
Christophe Reutenauer ◽  
Jean-Yves Thibon
Keyword(s):  
Hopf Algebras ◽  
Patterns In Permutations

scholarly journals Avoiding consecutive patterns in permutations

2010 ◽  
Vol 45 (3) ◽  
pp. 449-461 ◽  
Author(s):  
R.E.L. Aldred ◽  
M.D. Atkinson ◽  
D.J. McCaughan
Keyword(s):  
Patterns In Permutations

scholarly journals Consecutive patterns in permutations

2003 ◽  
Vol 30 (1-2) ◽  
pp. 110-125 ◽  
Author(s):  
Sergi Elizalde ◽  
Marc Noy
Keyword(s):  
Patterns In Permutations

scholarly journals (a,b)-rectangle patterns in permutations and words

2015 ◽  
Vol 186 ◽  
pp. 128-146 ◽  
Author(s):  
Sergey Kitaev ◽  
Jeffrey Remmel
Keyword(s):  
Patterns In Permutations
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