• Corpus ID: 239024340

The interval posets of permutations seen from the decomposition tree perspective

@inproceedings{Bouvel2021TheIP,
  title={The interval posets of permutations seen from the decomposition tree perspective},
  author={Mathilde Bouvel and Lapo Cioni and Benjamin Izart},
  year={2021}
}
The interval poset of a permutation is the set of intervals of a permutation, ordered with respect to inclusion. It has been introduced and studied recently in [Ten21]. We study this poset from the perspective of the decomposition trees of permutations, describing a procedure to obtain the former from the latter. We then give alternative proofs of some of the results in [Ten21], and we solve the open problems that it posed (and some other enumerative problems) using techniques from symbolic and… 

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SHOWING 1-10 OF 15 REFERENCES
Some Families of Trees Arising in Permutation Analysis
TLDR
A filtration of the set of permutations based on their strong interval trees is described, illustrating the convergence of analytic series towards a non-analytic limit at the level of the asymptotic behavior of their coefficients.
Simple permutations and pattern restricted permutations
TLDR
It is shown that, if the number of simple permutations in a pattern restricted class of permutations is finite, the class has an algebraic generating function and is defined by a finite set of restrictions.
Pattern Matching for Permutations
TLDR
A polynomial time algorithm is given for the decision problem, and the corresponding counting problem, in the case that P is separable—i.e. contains neither the subpattern (3,1, 4,2) nor its reverse, the sub pattern (2,4, 1,3).
An Introduction to the Moebius Function.
This is an introduction to the M\"obius function of a poset. The chief novelty is in the exposition. We show how order-preserving maps from one poset to another can be used to relate their M\"obius
Twenty-step algorithm for determining the asymptotic number of trees of various speces
The technique for finding the asymptotic number of unlabeled trees of various sorts was developed by Polya (1937) and perfected by Otter (1948). Modern presentations are available in the book of
Enumerative Combinatorics: Volume 1
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of
Analytic Combinatorics
TLDR
This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic.
The On-Line Encyclopedia of Integer Sequences
  • N. Sloane
  • Mathematics, Computer Science
    Electron. J. Comb.
  • 1994
TLDR
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
Permutation classes
This is a survey on permutation classes for the upcoming book Handbook of Enumerative Combinatorics.
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