MD  Matemàtica Discreta
http://hdl.handle.net/2117/3546
Sat, 13 Feb 2016 19:44:28 GMT
20160213T19:44:28Z

The conjugacy problem for freebycyclic groups
http://hdl.handle.net/2117/79985
The conjugacy problem for freebycyclic groups
Martino, Armando; Ventura Capell, Enric
We show that the conjugacy problem is solvable in [finitely
generated free]bycyclic groups, by using a result of O. Maslakova
that one can algorithmically find generating sets for the fixed sub
groups of free group automorphisms, and one of P. Brinkmann that
one can determine whether two cyclic words in a free group are
mapped to each other by some power of a given automorphism. The
algorithm effectively computes a conjugating element, if it exists. We
also solve the power conjugacy problem and give an algorithm to rec
ognize if two given elements of a finitely generated free group are
Reidemeister equivalent with respect to a given automorphism.
Thu, 26 Nov 2015 18:18:08 GMT
http://hdl.handle.net/2117/79985
20151126T18:18:08Z
Martino, Armando
Ventura Capell, Enric
We show that the conjugacy problem is solvable in [finitely
generated free]bycyclic groups, by using a result of O. Maslakova
that one can algorithmically find generating sets for the fixed sub
groups of free group automorphisms, and one of P. Brinkmann that
one can determine whether two cyclic words in a free group are
mapped to each other by some power of a given automorphism. The
algorithm effectively computes a conjugating element, if it exists. We
also solve the power conjugacy problem and give an algorithm to rec
ognize if two given elements of a finitely generated free group are
Reidemeister equivalent with respect to a given automorphism.

The automorphism group of a freebycyclic group in rank 2
http://hdl.handle.net/2117/79983
The automorphism group of a freebycyclic group in rank 2
Bogopolski, Oleg; Martino, Armando; Ventura Capell, Enric
Let
¡
be an automorphism of a free group
F
2
of rank
2 and let
M
¡
=
F
2
o
¡
Z
be the corresponding mapping torus of
¡
.
We prove that the group
Out
(
M
¡
) is usually virtually cyclic. More
over, we classify the cases when this group is Ønite depending on the
conjugacy class of the image of
¡
in
GL
2
(
Z
)
Thu, 26 Nov 2015 17:54:44 GMT
http://hdl.handle.net/2117/79983
20151126T17:54:44Z
Bogopolski, Oleg
Martino, Armando
Ventura Capell, Enric
Let
¡
be an automorphism of a free group
F
2
of rank
2 and let
M
¡
=
F
2
o
¡
Z
be the corresponding mapping torus of
¡
.
We prove that the group
Out
(
M
¡
) is usually virtually cyclic. More
over, we classify the cases when this group is Ønite depending on the
conjugacy class of the image of
¡
in
GL
2
(
Z
)

Absolutetype shaft encoding using LFSR sequences with a prescribed length
http://hdl.handle.net/2117/79981
Absolutetype shaft encoding using LFSR sequences with a prescribed length
Fuertes Armengol, José Mª; Balle Pigem, Borja de; Ventura Capell, Enric
Maximallength binary sequences have existed for a long time. They have many interesting properties, and one of them is that, when taken in blocks of n consecutive positions, they form 2n  1 different codes in a closed circular sequence. This property can be used to measure absolute angular positions as the circle can be divided into as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with an arbitrary length can be effectively designed with the minimal possible block length using linear feedback shift registers. Such sequences can be used to measure a specified exact number of angular positions using the minimal possible number of sensors that linear methods allow.
Thu, 26 Nov 2015 17:41:12 GMT
http://hdl.handle.net/2117/79981
20151126T17:41:12Z
Fuertes Armengol, José Mª
Balle Pigem, Borja de
Ventura Capell, Enric
Maximallength binary sequences have existed for a long time. They have many interesting properties, and one of them is that, when taken in blocks of n consecutive positions, they form 2n  1 different codes in a closed circular sequence. This property can be used to measure absolute angular positions as the circle can be divided into as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with an arbitrary length can be effectively designed with the minimal possible block length using linear feedback shift registers. Such sequences can be used to measure a specified exact number of angular positions using the minimal possible number of sensors that linear methods allow.

Absolute type shaft encoding using LFSR sequences with prescribed length
http://hdl.handle.net/2117/79980
Absolute type shaft encoding using LFSR sequences with prescribed length
Fuertes Armengol, José Mª; Balle, Borja; Ventura Capell, Enric
Maximallength binary sequences have been known for
a long time. They have many interesting properties, one of them
is that when taken in blocks of
n
consecutive positions they form
2
n
°
1 diÆerent codes in a closed circular sequence. This property
can be used for measuring absolute angular positions as the circle
can be divided in as many parts as diÆerent codes can be retrieved.
This paper describes how can a closed binary sequence with arbitrary
length be eÆectively designed with the minimal possible blocklength,
using
linear feedback shift registers
(LFSR). Such sequences can be
used for measuring a speciØed exact number of angular positions,
using the minimal possible number of sensors that linear methods
allow
Thu, 26 Nov 2015 17:28:19 GMT
http://hdl.handle.net/2117/79980
20151126T17:28:19Z
Fuertes Armengol, José Mª
Balle, Borja
Ventura Capell, Enric
Maximallength binary sequences have been known for
a long time. They have many interesting properties, one of them
is that when taken in blocks of
n
consecutive positions they form
2
n
°
1 diÆerent codes in a closed circular sequence. This property
can be used for measuring absolute angular positions as the circle
can be divided in as many parts as diÆerent codes can be retrieved.
This paper describes how can a closed binary sequence with arbitrary
length be eÆectively designed with the minimal possible blocklength,
using
linear feedback shift registers
(LFSR). Such sequences can be
used for measuring a speciØed exact number of angular positions,
using the minimal possible number of sensors that linear methods
allow

Completion and decomposition of a clutter into representable matroids
http://hdl.handle.net/2117/78129
Completion and decomposition of a clutter into representable matroids
Martí Farré, Jaume; Mier Vinué, Anna de
This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusionminimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.
Thu, 22 Oct 2015 11:23:00 GMT
http://hdl.handle.net/2117/78129
20151022T11:23:00Z
Martí Farré, Jaume
Mier Vinué, Anna de
This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusionminimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.

Fixed subgroups are compressed in surface groups
http://hdl.handle.net/2117/77518
Fixed subgroups are compressed in surface groups
Zhang, Qiang; Ventura Capell, Enric; Wu, Jianchun
For a compact surface Sigma (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix B, of any family B of endomorphisms of pi(1)(Sigma) is compressed in pi(1)(Sigma), i.e. rk(Fix B) <= rk(H) for any subgroup FixB <= H <= pi(1)(Sigma). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies that rk(Fix phi) <= rk(G) for every phi is an element of Aut(G).
Electronic version of an article published as International journal of algebra and computation, Vol. 25 (5), 2015, p. 865887
DOI: 10.1142/S0218196715500228 © [copyright World Scientific Publishing Company]
Thu, 08 Oct 2015 14:23:23 GMT
http://hdl.handle.net/2117/77518
20151008T14:23:23Z
Zhang, Qiang
Ventura Capell, Enric
Wu, Jianchun
For a compact surface Sigma (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix B, of any family B of endomorphisms of pi(1)(Sigma) is compressed in pi(1)(Sigma), i.e. rk(Fix B) <= rk(H) for any subgroup FixB <= H <= pi(1)(Sigma). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies that rk(Fix phi) <= rk(G) for every phi is an element of Aut(G).

Extensions and presentations of transversal matroids
http://hdl.handle.net/2117/77053
Extensions and presentations of transversal matroids
Bonin, Joseph; Mier Vinué, Anna de
A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (singleelement) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.; A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (singleelement) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.
Wed, 23 Sep 2015 12:44:05 GMT
http://hdl.handle.net/2117/77053
20150923T12:44:05Z
Bonin, Joseph
Mier Vinué, Anna de
A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (singleelement) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.
A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (singleelement) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.

On the diameter of random planar graphs
http://hdl.handle.net/2117/28378
On the diameter of random planar graphs
Chapuy, G.; Fusy, Éric; Giménez Llach, Omer; Noy Serrano, Marcos
We show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1) , in probability. More precisely, there exists a constant c > 0 such that {equation presented} for ˜ small enough and n = n0(˜). We prove similar statements for 2connected and 3connected planar graphs and maps.
Mon, 22 Jun 2015 17:34:47 GMT
http://hdl.handle.net/2117/28378
20150622T17:34:47Z
Chapuy, G.
Fusy, Éric
Giménez Llach, Omer
Noy Serrano, Marcos
We show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1) , in probability. More precisely, there exists a constant c > 0 such that {equation presented} for ˜ small enough and n = n0(˜). We prove similar statements for 2connected and 3connected planar graphs and maps.

Grouptheoretic orbit decidability
http://hdl.handle.net/2117/27428
Grouptheoretic orbit decidability
Ventura Capell, Enric
A recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely related to the study of the conjugacy problem for extensions of groups. In the present survey we explain several of the classical results closely
related to this concept, and we explain the main ideas behind the recent connection with the conjugacy problem made by Bogopolski–Martino–Ventura in [2]. All the consequences up to date, published in several other papers by other authors, are also commented and reviewed.
Fri, 17 Apr 2015 13:11:15 GMT
http://hdl.handle.net/2117/27428
20150417T13:11:15Z
Ventura Capell, Enric
A recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely related to the study of the conjugacy problem for extensions of groups. In the present survey we explain several of the classical results closely
related to this concept, and we explain the main ideas behind the recent connection with the conjugacy problem made by Bogopolski–Martino–Ventura in [2]. All the consequences up to date, published in several other papers by other authors, are also commented and reviewed.

An involution on bicubic maps and beta(0,1)trees
http://hdl.handle.net/2117/26140
An involution on bicubic maps and beta(0,1)trees
Claesson, Anders; Kitaev, Sergey; Mier Vinué, Anna de
Bicubic maps are in bijection with
(0
;
1)trees. We introduce two new
ways of decomposing
(0
;
1)trees. Using this we de ne an endofunc
tion on
(0
;
1)trees, and thus also on bicubic maps. We show that this
endofunction is in fact an involution. As a consequence we are able to
prove some surprising results regarding the joint equidistribution of cer
tain pairs of statistics on trees and maps. Finally, we conjecture the
number of xed points of the involution.
Wed, 28 Jan 2015 13:50:38 GMT
http://hdl.handle.net/2117/26140
20150128T13:50:38Z
Claesson, Anders
Kitaev, Sergey
Mier Vinué, Anna de
Bicubic maps are in bijection with
(0
;
1)trees. We introduce two new
ways of decomposing
(0
;
1)trees. Using this we de ne an endofunc
tion on
(0
;
1)trees, and thus also on bicubic maps. We show that this
endofunction is in fact an involution. As a consequence we are able to
prove some surprising results regarding the joint equidistribution of cer
tain pairs of statistics on trees and maps. Finally, we conjecture the
number of xed points of the involution.