Heuristics for the Sorting by Length-Weighted Inversions Problem on Signed Permutations

2014 ◽  
pp. 59-70 ◽  
Author(s):  
Thiago da Silva Arruda ◽  
Ulisses Dias ◽  
Zanoni Dias
Keyword(s):  
Signed Permutations

scholarly journals Restricted signed permutations counted by the Schröder numbers

2006 ◽  
Vol 306 (6) ◽  
pp. 552-563 ◽  
Author(s):  
Eric S. Egge
Keyword(s):  
Signed Permutations ◽  
Schröder Numbers

scholarly journals Diagrams and Essential Sets for Signed Permutations

10.37236/8106 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
David Anderson
Keyword(s):  
Schubert Variety ◽  
Signed Permutation ◽  
Signed Permutations ◽  
Degeneracy Locus ◽  
Essential Set ◽  
Diagrammatic Method ◽  
Essential Sets ◽  
Rank Conditions ◽  
Theoretic Version

We introduce diagrams and essential sets for signed permutations, extending the analogous notions for ordinary permutations.  In particular, we show that the essential set provides a minimal list of rank conditions defining the Schubert variety or degeneracy locus corresponding to a signed permutation.  Our essential set is in bijection with the poset-theoretic version defined by Reiner, Woo, and Yong, and thus gives an explicit, diagrammatic method for computing the latter.

Heuristics for the Sorting Signed Permutations by Reversals and Transpositions Problem

2018 ◽  
pp. 65-75
Author(s):  
Klairton Lima Brito ◽  
Andre Rodrigues Oliveira ◽  
Ulisses Dias ◽  
Zanoni Dias
Keyword(s):  
Signed Permutations

Pairings and Signed Permutations

2006 ◽  
Vol 113 (7) ◽  
pp. 642 ◽  
Author(s):  
Valerio De Angelis
Keyword(s):  
Signed Permutations

scholarly journals The sorting index on colored permutations and even-signed permutations

2015 ◽  
Vol 68 ◽  
pp. 18-50 ◽  
Author(s):  
Sen-Peng Eu ◽  
Yuan-Hsun Lo ◽  
Tsai-Lien Wong
Keyword(s):  
Signed Permutations ◽  
Colored Permutations

Signed permutations and the braid group

2017 ◽  
Vol 47 (2) ◽  
pp. 391-402
Author(s):  
Michael P. Allocca ◽  
Steven T. Dougherty ◽  
Jennifer F. Vasquez
Keyword(s):  
Braid Group ◽  
Signed Permutations

scholarly journals COMPUTING SIGNED PERMUTATIONS OF POLYGONS

2011 ◽  
Vol 21 (01) ◽  
pp. 87-100
Author(s):  
GREG ALOUPIS ◽  
PROSENJIT BOSE ◽  
ERIK D. DEMAINE ◽  
STEFAN LANGERMAN ◽  
HENK MEIJER ◽  
...  
Keyword(s):  
Mirror Symmetry ◽  
Time Algorithm ◽  
Worst Case ◽  
Signed Permutations ◽  
Np Complete ◽  
Edge List ◽  
The Given ◽  
Special Case ◽  
Planar Polygon

Given a planar polygon (or chain) with a list of edges {e1, e2, e3, …, en-1, en}, we examine the effect of several operations that permute this edge list, resulting in the formation of a new polygon. The main operations that we consider are: reversals which involve inverting the order of a sublist, transpositions which involve interchanging subchains (sublists), and edge-swaps which are a special case and involve interchanging two consecutive edges. When each edge of the given polygon has also been assigned a direction we say that the polygon is signed. In this case any edge involved in a reversal changes direction. We show that a star-shaped polygon can be convexified using O(n2) edge-swaps, while maintaining simplicity, and that this is tight in the worst case. We show that determining whether a signed polygon P can be transformed to one that has rotational or mirror symmetry with P, using transpositions, takes Θ(n log n) time. We prove that the problem of deciding whether transpositions can modify a polygon to fit inside a rectangle is weakly NP-complete. Finally we give an O(n log n) time algorithm to compute the maximum endpoint distance for an oriented chain.

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