Algeria, Sidi Bel Abbès

236 Pages·2015·5.69 MB·English

Conference-School on Discrete Mathematics and Computer Science
Algeria, Sidi Bel Abbès
November15-19,2015.
Publishedby:
RecitsLaboratory
FacultyofMathematics
USTHB
http://www.lrecits.usthb.dz/activites.htm
ISBN:X-XXXX-XXXXXX
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usingLATEX’s‘confproc’package,version0.8
PrintedinAlgiers—November2015
ProgramCommittee OrganizationCommittee
A.Bouyakoub,OranIUniv.,Algeria,Chair A.Yousfate,SBAUniv.,Chair
M.AlZohairi,KSU,SaudiaArabia B.Belarbi,OranIUniv.,
N.Badache,USTHB,Algeria H.Belbachir,USTHB,
M.Bekkali,FezUniv.,Morocco A.Belkhir,USTHB,
H.Belbachir,USTHB,Algeria M.Benchohra,SBAUniv.,
M.A.Benoumhani,M’SilaUniv.,Algeria S.Boukli-Hacène,SBAUniv.,
I.Boudabbous,SfaxUniv.,Tunisia I.-E.Bousbaa,USTHB,
Y.Boudabbous,KFU,SaudiaArabia A.Bouyakoub,OranIUniv.,
M.Boudhar,USTHB,Algeria B.Chafi,SBAUniv
M.E.-A.Chergui,USTHB,Algeria H.Harik,CERIST,
A.Dil,AkdenizUniv.,Turkey M.Lakrib,SBAUniv.,
A.ElSahili,LebaneseUniv.,Lebanon E.Lamini,CDTA
K.M.Faraoun,SBAUniv.,Algeria M.Mechab,SBAUniv.,
O.Khadir,MohammadiaUniv.,Morocco F.Tebboune,SaidaUniv.
H.Kheddouci,LyonIUniv.,France
E.Kiliç,TOBBUniv. Turkey
T.Komatsu,WuhanUniv.,China
J.-G.Luque,RouenUniv.,France
M.Mihoubi,USTHB,Algeria
A.Mokrane,Paris8Univ.,France
M.Pouzet,CalgaryUniv.,Canada
S.Pirzada,KashmirUniv.,India
H.SiKaddour,LyonIUniv.,France
L.Szalay,SopronUniv.,Hungary
N.Thiéry,Paris11Univ.,France
A.Yousfate,SBAUniv.,Algeria
D.Ziadi,RouenUniv.,France
Conference-SchoolonDiscreteMathematicsandComputerScience,Algeria,SidiBelAbbès,November15-19,2015.
CONFERENCE PROGRAM
Day 1
PlenaryConference
1 NémethLÁSZLÓ
HyperbolicPascaltrianglesandpyramid
5 TaharMOURID
StatisticsofFunctionalAutoregressiveProcesses
OralSession-EnumerativeCombinatorics
6 NesrineBENYAHIA-TANI
Orderedandnon-orderednon-congruentconvexquadrilateralsinscribedinaregularn-gon
9 AssiaFettoumaTEBTOUB
The2-successiveEuleriannumbersandunimodality
12 AliCHOURIA
Thebosonnormalorderingproblem: Combinotorialinterpretation
OralSession-GraphTheory
16 MohammedYAGOUNI
Meta-Storming,unoutilpourlamiseenœuvrecollaborativedesMtaheuristiques
19 AymenBENAMIRA
Reconstructionofdigraphsuptocomplementation
22 DaouyaLAICHE
Packingcoloringofsomeundirectedandorientedcoronaegraphs
PlenaryConference
26 FairouzTCHIER
SometopicsinDiscreteMathematics
29 ImedBOUDABBOUS
Thenon 2 -recognizableindecomposabletournaments
{− }
OralSession-Arithmetics
32 AminaSOUYAH
Imageencipheringschemes: Stateoftheart
36 SamiaMASROUR
Nesteddoublebinomialsums
DIMACOS-iii
Conference-SchoolonDiscreteMathematicsandComputerScience,Algeria,SidiBelAbbès,November15-19,2015.
39 DjamelBERKANE
Onaconstantrelatedtotheprimecountingfunction
OralSession-GraphTheory
41 MounaYAICH
Graphesindécomposablesetleurssous-graphesindécomposablesà7ouà8sommets
44 RahmaSALEM
Hereditarilyhemimorphyof k -hemimorphicdigraphsfork 8
{− } ≥
48 NourElHoudaAsmaMERABET
nOutofnAudiblePasswordSecretSharingSchemeWithUnexpandedShares
Day 2
PlenaryConference
52 MoussaBENOUMHANI
Polynomialassociatedwithfinitetopologies
55 SzalayLÁSZLÓ
Arithmeticaltriangles
OralSession-EnumerativeCombinatorics
58 AthmaneBENMEZAI
Chu-Vandermondeidentityforq-analogueand p,q-analogueofbisnomialcoefficients
61 SaidAMROUCHE
TrianglesarithmétiquesassociéesauxsuitesdeFibonaccigénéralisées
64 OussamaIGUEROUFA
CentralBisnomialCoefficientsonHypergrids
OralSession-GraphTheoryandRelationalStructures
69 DjamilaOUDRAR
Monomorphicdecompositionandprofile
73 BrahimBENMEDJDOUB
Colorationdincidencesetdescarrésdesgraphescirculantsetdesgraphesdistances
77 FatmaMESSOUDI
Theupperpaired-dominationsubdivisionnumbersofgraphs
PlenaryConference
79 OmarKHADIR
AttacksonElGamaldigitalsignaturescheme: anoverview
DIMACOS-iv
Conference-SchoolonDiscreteMathematicsandComputerScience,Algeria,SidiBelAbbès,November15-19,2015.
OralSession-OperationalResearch
81 NourElHoudaTELLACHE
Schedulingthetwo-machineflowshopproblemwithunit-timeoperationsandconflictgraph
85 MohamedBOUALEM
StochasticAnalysisandBoundsfortheStationaryDistributionofanM/G/1RetrialQueuewithBreakdowns
88 NadjatMEZIANI
PSOandSimulatedannealingforthetwomachinesflowshopschedulingproblemwithcoupled-operations
91 AminaHANED
Schedulingwithpreemptionandsetuptimes
OralSession-GraphTheory
95 MariaABIAAD
Pathsintournaments
97 MohamedAmineBOUTICHE
Forwardingindicesofsomegraphoperations
101 HakimHARIK
Onbandwidthofsomeclassesofgraphs
103 MortadaMAIDOUN
Theb-ChromaticNumberand f-ChromaticVertexNumberofRegularGraphs
Day 4
PlenaryConference
106 HamidABCHIR
Coloriagedesnoeuds
108 ShariefuddinPIRZADA
SumoftheLaplacianeigenvaluesofagraphandBrouwer’sconjecture
OralSession-OperationalResearch
111 KarimAMROUCHE
Résolutionapprochéed’unproblèmed’ordonnancementdetypeflowshopcontinuavecrecirculation
113 ZahiaBOUABBACHE
Optimalcontrolofdynamicsystemswithrandominput
116 SlimaneBELLAOUAR
TowardsaSet-StringSubsequenceKernel
OralSession-EnumerativeCombinatorics
120 AmineBELKHIR
Statisticonlineartilingsandgeneralizedq-Fibonaccipolynomials
123 MouradRAHMANI
SomeresultsonCauchynumbers
DIMACOS-v
Conference-SchoolonDiscreteMathematicsandComputerScience,Algeria,SidiBelAbbès,November15-19,2015.
124 ImèneBENRABIA
TilinginterpretationforcombinatorialidentityassociatedtoorderthreeFibonaccisequence
PlenaryConference
126 FayçalHAMDI
Modelingtheperiodicconditionalvolatilityasamixtureprocess
OralSession-StochasticProcesses
128 BillelALIAT
PeriodicstationarityandexistenceofmomentsofMarkov-switchingPARMAprocesses
132 RokiaHEMIS
EstimationBayesienned’unMelangedeModélesGARCHPériodiquesparlaMéthodedeGriddy-Gibbs
134 NadiaBOUSSAHA
Periodicmultivariatestochasticvolatilitymodel: structureandestimation
136 NesrineKARATERKI
InégalitésdeGrandesDéviationsdel’EstimateurSievesd’unOpérateurdunProcessusARFonctionel
OralSessionEnumerativeandAlgebraicCombinatorics
138 BoudekhilCHAFI
Surlesfonctionsholomorphesdiscrèetes
141 ZakariaCHEMLI
Shifteddominotableaux
143 MoussaAHMIA
OntheweightedsumsassociatedtoraysinPascal’striangle
145 FarizaKRIM
RecurrencesassociatedtoraysinnegativeGeneralizedArithmeticTriangle
PlenaryConference
148 Nour-EddineFAHSSI
TheManyAspectsofPolynomialTriangles
OralSession-MathematicalProgramming
152 YounesGUELLOUMA
TowardsIntegralsofRationalTreeExpressions
156 AmelBELABBACI
Approchepourl’optimisationd’unefonctionquadratiqueindéfinie
159 SlimaneOULAD-NAOUI
FrequentPatternMining: aReductiontoAcyclicWeightedAutomataDeterminisation
OralSession-EnumerativeCombinatorics
164 MohammedSaidMAAMRA
NoteonsomerestrictedStirlingnumbersofthesecondkind
167 ImadEddineBOUSBAA
TheGeneralizedr-LahNumbersRevisited
DIMACOS-vi
Conference-SchoolonDiscreteMathematicsandComputerScience,Algeria,SidiBelAbbès,November15-19,2015.
170 YaminaSAIDI
AnidentityonpairsofAppell-typepolynomials
Day 5
PlenaryConference
173 AyhanDIL
GeneralizedGeometricPolynomialsandApplicationstoSerieswithZetaValues
176 AbdelghaniOUAHAB
ExistenceandCompactnessResultsforSystemofDifferenceEquations
OralSession-EnumerativeCombinatorics
181 AssiaMEDJERREDINE
AssociatedStirlingnumbersforsomefamiliesofgraphs
185 AsmaaRAHIM
Ther-Jacobi-Stirlingnumbersofthesecondkind
189 AbdelghaniMEHDAOUI
TheStirlingNumberswithconstraint
OralSession-StochasticProcesses
192 TayebBLOUHI
ExistenceResultsforCoupleStochasticDifferenceEquationswithDelay
197 WahibaBOUABSA
Someasymptoticnormalityresultofk-NearestNeighborestimator
200 AhmedBOUDAOUI
ExistenceofmildsolutionstostochasticdelayevolutionequationswithafractionalBrownianmotionandimpulses
204 MeriemTIACHACHAT
SomeapplicationsofthetranslatedWhitneynumbers
PosterSession
206 MohammedBENATALLAH
b-Domaticnumberofthejoingraphs
209 AbdelkaderHAMTAT
OntheDiophantineequationx2+13k=yn
212 TassaditLACHEMOT
AnMX/G/1retrialqueuewithbreakdown,repair,lossandtwoTYPESofcustomers
214 BoubakerMECHAB
Asymptoticnormalityofhighriskestimateforfunctionaldata
218 SelmaMERADJI
Thelocaltimeundersublinearexpectationsandapplications
220 SaraSTIHI
Stochasticcalculusformatrixfractionalbrownianmotionandapplications
DIMACOS-vii
Conference-SchoolonDiscreteMathematicsandComputerScience,Algeria,SidiBelAbbès,November15-19,2015.
222 NesrineZIDANI
Approximationofmultiserverretrialqueuesbyvalueextrapolationtechnique
224 AsmaBENCHEKOR
Processussemi-markoviensàtempsdiscret. Théorieetapplications
227 List of Authors
DIMACOS-viii
ConferenceonDiscreteMathematicsandComputerScience,SidiBelAbbess,Algeria,November15-19,2015
Hyperbolic Pascal triangles and pyramid
Ne´meth, La´szlo´
University of West Hungary, Institute of Mathematics
Ady E. u´t 5., Sopron, Hungary
[email protected]
Abstract
WeintroduceanewgeneralizationofPascal’striangleandpyramidbasedonthehyperbolicregularmosaics
inplaneandspace. Thenwestudycertainquantitativeproperties.
Keywords: Pascaltriangle,Pascalpyramid,regularmosaicsonhyperbolicplane,cubemosaicinhyperbolicspace
2010MathematicsSubjectClassification: 11B99,05A10.
1. Hyperbolic Pascal triangles
ThereareseveralapproachestogeneralizethePascal’sarithmetictriangle(see,forinstance[3,4]). Anewtypeofvariations
ofitisbasedonthehyperbolicregularmosaicsdenotedbySchla¨fli’ssymbol p,q ,where(p 2)(q 2) > 4([5]). Each
{ } − −
regularmosaicinducesasocalledhyperbolicPascaltriangle(see[2]),followingandgeneralizingtheconnectionbetweenthe
classicalPascal’striangleandtheEuclideanregularsquaremosaic 4,4 . Formoredetailssee[2],butherewealsocollect
{ }
somenecessaryinformation.
ThehyperbolicPascaltrianglesbasedonthemosaic p,q canbefiguredasadigraph,wheretheverticesandtheedges
{ }
are the vertices and the edges of a well defined part of the lattice p,q , respectively, and the vertices possess a value that
{ }
givethenumberofthedifferentshortestpathsfromthebasevertex. Figure1illustratesthehyperbolicPascaltrianglewhen
p,q = 4,5 . Herethebasevertexhastwoedges,theleftmostandtherightmostverticeshavethree,theothershavefive
{ } { }
edges. The quadrilateral shape cells surrounded by the appropriate edges correspond to the squares in the mosaic. Apart
fromthewingerelements,certainvertices(called“TypeA”)have2ascendantsand3descendants,whiletheothers(“Type
B”) have 1 ascendant and 4 descendants. In the figures we denote the vertices type A by red circles and the vertices type
B bycyandiamonds, furtherthewingersbywhitediamonds. Theverticeswhicharen-edge-longfarfromthebasevertex
areinrown. Thegeneralmethodofpreparingthegraphisthefollowing: wegoalongtheverticesofthejth row,according
to the type of the elements (winger, A, B), we draw the appropriate number of edges downwards (2, 3, 4, respectively).
Neighbouredgesoftwoneighbourverticesofthejth rowmeetinthe(j +1)th row,constructinganewvertextypeA. The
otherdescendantsofrowj havetypeB inrowj+1. Inthesequel,)n(denotesthekth elementinrown,whichiseitherthe
k
sumofthevaluesofitstwoascendantsorthevalueofitsuniqueascendant. Wenote,thatthehyperbolicPascaltriangleshas
thepropertyofverticalsymmetry.
In studying the quantitative properties of the hyperbolic Pascal triangle 4,q , first we determine the number of the
{ }
elementsofthenth rowofthegraph. Denotebya andb thenumberofverticesoftypeAandB,respectively,furtherlet
n n
s =a +b +2,whichgivesthetotalnumberoftheverticesofrown 1. Recall,thatq 5.
n n n
≥ ≥
Theorem 1. The three sequences an , bn and sn can be described by the same ternary homogeneous recurrence
{ } { } { }
relation
x =(q 1)x (q 1)x +x (n 4),
n n 1 n 2 n 3
− − − − 1 − − ≥
ConferenceonDiscreteMathematicsandComputerScience,SidiBelAbbess,Algeria,November15-19,2015
Figure1: HyperbolicPascaltrianglelinkedto 4,5 uptorow5
{ }
theinitialvaluesare
a =0,a =1,a =2, b =0,b =0,b =q 4, s =2,s =3,s =q.
1 2 3 1 2 3 1 2 3
−
Let aˆ ,ˆb and sˆ denote the sum of type A, type B and all elements of the nth row, respectively. We will justify the
n n n
followingstatements.
Theorem2. Thethreesequences aˆn , ˆbn and sˆn canbedescribedbythesameternaryhomogenousrecurrencerelation
{ } { } { }
x =qx (q+1)x +2x (n 4),
n n 1 n 2 n 3
− − − − ≥
theinitialvaluesare
aˆ =0, aˆ =2, aˆ =6, ˆb =0, ˆb =0, ˆb =2(q 4), sˆ =2, sˆ =4, sˆ =2q.
1 2 3 1 2 3 1 2 3
−
Lets bethealternatingsumofelementsofthehyperbolicPascaltriangles(startingwithpositivecoefficient)inrown,
n
andwedistinguishtheevenandoddcases.
e
Theorem3. Letqbeeven. Then
sn =sn−1(−1)i)ni(= 2(5 q0),t−1+2, iiff nn==22tt,+1, nn≥12,,
i=0 (cid:26) − − ≥
X
e
hold,furthers =1.
0
Theorem4. eLetq ≥5beodd. Thens0 =1,further
s =sn−1( 1)ei)n(= ( 2)t(q 0,5)t 1+2, iiff nn==33tt+11,, nn≥1n,,
n − i  − − − − ≥ 1
Xi=0  2(−2)t(q−5)t−1+2, if n=3t, n≥n2,
e
where(n ,n )=(2,3)and(5,6)ifn>5andn=5,respectively. Inthelattercases =0,s = 2.
1 2 2 3
−
e e
2