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SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2016, Volume 30, Issue 3, pp. 1660 - 1684
In this paper, we introduce plane permutations, i.e., pairs p - (s, pi), where s is an n-cycle and pi is an arbitrary permutation, represented as a two-row... 
Reversal | Transposition | Exceedance | Hypermap | Stirling number of the first kind | Plane permutation | MATHEMATICS, APPLIED | SIGNED PERMUTATIONS | ALGORITHM | plane permutation | TRANSPOSITIONS | transposition | reversal | BLOCK-INTERCHANGES | REVERSALS | GENOME REARRANGEMENTS | exceedance | hypermap
Journal Article
JOURNAL OF UNIVERSAL COMPUTER SCIENCE, ISSN 0948-695X, 2019, Volume 25, Issue 2, pp. 98 - 121
For estimating the evolutionary distance between genomes of two different organisms, many sorting permutation problems have emerged. A well accepted way to do... 
Genome rearrangements | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Reversals | SIGNED PERMUTATIONS | Transpositions | Computational Biology | Sorting permutations | APPROXIMATION ALGORITHM | 1.375-APPROXIMATION ALGORITHM | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 06/2018, Volume 97, pp. 1 - 26
It is a classical result that the parity-balance of the number of weak excedances of all permutations (derangements, respectively) of length is the Euler... 
Derangements | Euler number | Weighted bicolored Motzkin paths | Continued fractions | Springer number | Signed permutations | POLYNOMIALS | MATHEMATICS, APPLIED | ENUMERATION | CROSSINGS | SNAKES
Journal Article
Discrete Mathematics, ISSN 0012-365X, 09/2017, Volume 340, Issue 9, pp. 2161 - 2182
In this paper, we present a topological framework for studying signed permutations and their reversal distance. This framework is based on a presentation of... 
Fatgraph | Poincaré dual | Reversal distance | [formula omitted]-map | Signed permutation | π-map | MATHEMATICS | pi-map | RNA | Poincare dual | REVERSALS | CLASSIFICATION | ALGORITHMS | TRANSPOSITIONS
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 09/2018, Volume 25, Issue 3
We introduce diagrams and essential sets for signed permutations, extending the analogous notions for ordinary permutations. In particular, we show that the... 
Essential set | Rank condition | Schubert variety | Signed permutation | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | SCHUBERT
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 03/2018, Volume 715, pp. 35 - 59
Comparative genomics is a line of study which aims at determining dis/similarities between genomes. One way of doing this is to infer the large scale mutations... 
Genome rearrangements | Prefix rearrangements | Approximation algorithms | Reversals | Transpositions | Diameter | SIGNED PERMUTATIONS | DISTANCE | BOUNDS | SUFFIX REVERSALS | 1.375-APPROXIMATION ALGORITHM | COMPUTER SCIENCE, THEORY & METHODS | PREFIX REVERSALS | Bioinformatics | Data Structures and Algorithms | Computer Science | Computational Complexity
Journal Article
Journal of Bioinformatics and Computational Biology, ISSN 0219-7200, 02/2017, Volume 15, Issue 1
Some interesting combinatorial problems have been motivated by genome rearrangements, which are mutations that affect large portions of a genome. When we... 
reversals | Permutations | diameter | prefix | sorting | transpositions | approximation algorithms | suffix | SIGNED PERMUTATIONS | ALGORITHM | MATHEMATICAL & COMPUTATIONAL BIOLOGY
Journal Article
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, ISSN 0035-7596, 2017, Volume 47, Issue 2, pp. 391 - 402
We make a connection between the braid group and signed permutations. Using this link, we describe a commutative diagram which contains the fundamental... 
MATHEMATICS | signed permutation | symmetric group | Braid group
Journal Article
Discrete Mathematics, ISSN 0012-365X, 05/2014, Volume 323, Issue 1, pp. 49 - 57
The purpose of this paper is to establish a connection between alternating runs of signed permutations in the hyperoctahedral group and left peaks of... 
Peaks | Up signed permutations | Valleys | Alternating runs | POLYNOMIALS | MATHEMATICS | NUMBER | ENUMERATION | Permutations | Mathematical analysis | Group theory | Joining | Polynomials | Joints | Combinatorial analysis | Counting
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2018, Volume 235, pp. 59 - 80
It is well-known that signed permutations can be sorted in polynomial time, while sorting unsigned ones is an -hard problem. Although sorting signed... 
Average number of reversals | Combinatorics of permutations | Sorting signed permutations by reversal | MATHEMATICS, APPLIED | DISTANCE | GENETIC ALGORITHM | Studies | Lower bounds | Permutations | Algorithms | Computation | Upper bounds | Probability | Graphs | Polynomials | Combinatorial analysis
Journal Article
Results in Mathematics, ISSN 1422-6383, 6/2018, Volume 73, Issue 2, pp. 1 - 13
In the study of enumeration polynomials of signed permutations of rank n, which is known as a Coxeter group of type B, Chow and Ma found that alternating runs... 
type D permutations | up signed permutations | Alternating runs | Mathematics, general | Mathematics | peaks | valleys | Primary 05A05 | Secondary 05A15 | MATHEMATICS | MATHEMATICS, APPLIED | SIGNED PERMUTATIONS | NUMBER | EULERIAN POLYNOMIALS | Information science
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 02/2017, Volume 24, Issue 1
We consider the classical Mahonian statistics on the set B-n(Sigma) of signed permutations in the hyperoctahedral group B-n which avoid all patterns in Sigma,... 
Major index | Generating function | Inversion statistic | Pattern avoiding permutations | Signed permutations | MATHEMATICS | MATHEMATICS, APPLIED | major index | generating function | inversion statistic | signed permutations | pattern avoiding permutations
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 05/2017, Volume 86, pp. 1 - 18
Permutation tableaux were introduced by Steingrímsson and Williams. Corteel and Kim defined the sign of a permutation tableau in terms of the number of... 
Bijection | Permutation tableau | Weak excedance | Sign-imbalance | Signed permutation | Symmetric permutation | MATHEMATICS, APPLIED | COMBINATORICS
Journal Article
Journal of Computational Biology, ISSN 1066-5277, 2001, Volume 8, Issue 5, pp. 483 - 491
Journal Article
BMC GENOMICS, ISSN 1471-2164, 11/2011, Volume 12, Issue Suppl 3, pp. S26 - S26
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 01/2011, Volume 46, Issue 1-4, pp. 209 - 225
In this paper we outline a approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of... 
Permutations | Crossings | Orthogonal polynomials | Permutation tableaux | Rook placements | Moments | Signed permutations | Genocchi numbers | MATHEMATICS, APPLIED | ALIGNMENTS | TABLEAUX | ASYMMETRIC EXCLUSION PROCESS | COMBINATORICS | Matrices | Enumeration | Mathematical analysis | Matrix methods | Combinatorial analysis
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 21, pp. 6235 - 6244
In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations. We use this structure to derive the generating... 
Labeled partition | [formula omitted]-derangement number | Colored permutation | Flag major index | q-derangement number | Q-DERANGEMENT NUMBERS | MATHEMATICS | WREATH-PRODUCTS | SIGNED WORDS
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 08/2014, Volume 59, pp. 26 - 47
One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type is the set of the alternating permutations and in type... 
Sign imbalance | Alternating permutation | Valley-signed permutation | Snake | Inversions | MATHEMATICS, APPLIED | POSETS | SPRINGER NUMBERS | PARTITION SHAPES | COMBINATORICS | ALTERNATING PERMUTATIONS | Permutations | Mathematical analysis | Statistics | Snakes | Combinatorial analysis
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 10, pp. 3310 - 3317
A family of sets is said to be - if any two sets in contain at least common elements. A -intersecting family is said to be if there are at least elements... 
Signed set | Permutation | Intersecting family | Erdős–Ko–Rado | Erdo{double acute}s-Ko-Rado | MATHEMATICS | KO-RADO THEOREM | INTEGER SEQUENCES | SYSTEMS | Erdos-Ko-Rado | FINITE SETS | GRAPHS
Journal Article
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