組合理論與算法研討會(huì)

組合理論與算法研討會(huì)會(huì)議手冊(cè)2023年4月21日-24日中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院數(shù)學(xué)機(jī)械化重點(diǎn)實(shí)驗(yàn)室，北京會(huì)議信息時(shí)間：2023年4月21日-24日（21日?qǐng)?bào)到，地點(diǎn)數(shù)學(xué)院南樓204）地點(diǎn)：北京中關(guān)村東路55號(hào)中國(guó)科學(xué)院數(shù)學(xué)院南樓204會(huì)議室會(huì)議日程會(huì)議報(bào)到：2023年4月21日下午2點(diǎn)-6點(diǎn)，南樓2042023年4月22日周六學(xué)術(shù)報(bào)告（南樓204會(huì)議室）時(shí)間日程演講人8:20-8:30簽到8:30-8:40開(kāi)幕8:40-8:50特邀學(xué)者講話王軍8:50-9:50置換與加法組合I孫智偉9:50-10:20合影與茶歇10:20-10:50組合、圖論學(xué)在物理、化學(xué)、統(tǒng)計(jì)上的應(yīng)用葉永南10:50-11:20Amultipleq-translationformula劉治國(guó)11:20-11:50Abel引理與q-級(jí)數(shù)變換馬欣榮11:50-12:20非交換基本超幾何級(jí)數(shù)導(dǎo)引張之正12:30-13:30午餐（物科賓館自助）14:00-15:00AnalyticAspectsofCombinatorialSequencesI王毅15:00-16:00AnalyticAspectsofCombinatorialSequencesII王毅16:00-16:20茶歇16:20-16:50Kazhdan-Lusztigpolynomialsofcompletegraphs楊立波16:50-17:20Thestabilityofmultivariatepolynomialsequences劉麗17:20-17:50EhrhartTheoryonLatticePathMatroids范久瑜18：00-20：00晚宴（物科賓館）2023年4月23日周日（南樓204會(huì)議室）時(shí)間日程演講人8:30-9:30AnalyticAspectsofCombinatorialSequencesIII王毅9:30-10:30AnalyticAspectsofCombinatorialSequencesIV王毅10:30-10:50茶歇10:50-11:20FurtherExtensionsofHaglund-Remmel-WilsonIdentity嚴(yán)慧芳11:20-11:50OnlatticepathsandtheThue-Morsesequence傅士碩12:00-13:30午餐（物科賓館自助）14:00-15:00置換與加法組合II孫智偉15:00-16:00置換與加法組合III孫智偉16:00-16:20茶歇16:20-16:50完全對(duì)稱多項(xiàng)式零點(diǎn)的新下界張俊16:50-17:20Furtherq-supercongruencesfromatransformationofRahman郭軍偉17:20-17:50OnaconjectureofTokushigeforcross-t-intersectingfamilies張華軍18：00-20：00晚餐（物科賓館）2023年4月24日周一（南樓204會(huì)議室）時(shí)間日程演講人8:30-9:30置換與加法組合IV孫智偉9:30-9:50茶歇9:50-10:20ModularityofNahmSumsfortheTadpoleDiagram王六權(quán)10:20-10:50Generalizedq-partialdifferentialequationsforq-3Dhypergeometricpolynomialsandsomeapplications曹健10:50-11:20Symmetriesinparkingfunctions,Dyckpathsandtrees林志聰11:30-14:00午餐(物科賓館)14:00-17:00自由討論報(bào)告信息題目1：置換與加法組合報(bào)告人：孫智偉教授（南京大學(xué)）

摘要：與Abel群加法結(jié)構(gòu)有關(guān)的加法組合是組合和數(shù)論的交叉領(lǐng)域，國(guó)際上這方面的研究十分活躍。本課程討論有關(guān)的置換與和集問(wèn)題，介紹這方面的已有結(jié)果與研究方法，還將提及一些未解決問(wèn)題。題目2：組合、圖論學(xué)在物理、化學(xué)、統(tǒng)計(jì)上的應(yīng)用

報(bào)告人：葉永南教授（溫州大學(xué)）

摘要：在這個(gè)演講裏。我將用淺顯的語(yǔ)言簡(jiǎn)單介紹過(guò)去我用組合、圖論在物理、化學(xué)、統(tǒng)計(jì)等跨學(xué)科領(lǐng)域的一些應(yīng)用。題目3：Amultipleq-translationformula

報(bào)告人：劉治國(guó)教授（華東師范大學(xué)）

摘要：Inthistalk,weshallintroduceamultipleq-exponentialdifferentialoperationalidentityfortheanalyticfunctionsinseveralvariables,whichcanberegardedasamultipleq-translationformula.Thismultipleq-translationformulaisafundamentalresultandplayapivotalroleinq-mathematics.Usingthisformula,wecaneasilyrecovermanyclassicalconclusionsinq-mathematicsandderivesomenewq-formulas.題目4：Abel引理與q-級(jí)數(shù)變換

報(bào)告人：馬欣榮教授（蘇州大學(xué)）

摘要：ThistalkisaboutthreenewandgeneraltransformationswithsixteenparametersandbasesviaAbel'slemmaonsummationbyparts.Astheirapplications,wewillexhibitsomenewtransformationsofbasichypergeometricseries.AmongincludesomenewresultsofGasperandRahman'squadratic,cubic,andquartictransformations.Furthermore,weputforwardtheso-calledR,S-typetransformationwitharbitrarydegreetounifysuchmultibasictransformations.Somespecial題目5：非交換基本超幾何級(jí)數(shù)導(dǎo)引

報(bào)告人：張之正教授（洛陽(yáng)師范學(xué)院）

摘要：在本報(bào)告中，將從Gauss非交換二項(xiàng)式定理出發(fā)，介紹一般非交換基本超幾何級(jí)數(shù)的基本概念及基本結(jié)果。題目6：Analyticaspectsofcombinatorialsequences

報(bào)告人：王毅教授（大連理工大學(xué)）

摘要：Inthistalk,wediscusssomeanalyticpropertiesofcombinatorialsequences.題目7：Kazhdan-Lusztigpolynomialsofcompletegraphs

報(bào)告人：楊立波教授（南開(kāi)大學(xué)）

摘要：Recently,LuisFerroniandMattLarsonprovideacombinatorialinterpretationofKazhdan–Lusztigpolynomialsofcompletegraphs.Inparticular,theyconfirmaconjectureofElias,ProudfootandWake?eldonthetopcoefficientsofKazhdan–Lusztigpolynomialsofcompletegraphs.InthistalkwewillshowhowtodeterminethetopcoefficientsofinverseKazhdan–LusztigpolynomialsofcompletegraphsbasedonFerroniandLarson'swork.題目8：Aunifiedapproachtomultivariatepolynomialsequenceswithrealstability

報(bào)告人：劉麗教授（曲阜師范大學(xué)）

摘要：Wegivesomenewsufficientconditionsforasequenceofmultivariatepolynomialstoberealstable.Asapplications,weobtaintherealstabilityofmanyimportantmultivariatepolynomials,suchasmultivariateEulerianpolynomials,multivariateBellpolynomialsandmultivariatepolynomialsoverStirlingpermutationsinaunifiedmanner.Andwealsoshowsomenewresults,suchastherealstabilityofmultivariatepolynomialsoverJacobi-Stirlingpermutations,andtheproperpositionpropertyofmultivariatematchingpolynomials.題目9：EhrhartTheoryonLatticePathMatroids

報(bào)告人：范久瑜副教授（四川大學(xué)）

摘要：WewillgiveasurveyoftheEhrharttheoryoflatticepathmaroidsandreportourrecentprogressonthistopic.題目10：FurtherExtensionsofHaglund-Remmel-WilsonIdentity

報(bào)告人：嚴(yán)慧芳教授（浙江師范大學(xué)）

摘要：MacMahon'sequidistributiontheoremstatesthatthepermutationstatisticsinversionnumberandmajorindexareequidistributed.In2015,RemmelandWilsonprovedaconjecturedidentityofHaglundwhichisanextensionofMacMahon'sequidistributiontheoremtoorderedsetpartitions.Recently,Liuextendedthisidentitytok-Stirlingpermutationsandposedaconjectureconcerninganascentanalogueofhisextension.Inthistalk,weshallpresentacombinatorialproofofthisconjecture.Furthermore,wederiveananalogousresultforanothermaj-likestatisticintroducedbyLiu.ThistalkisbasedonjointworkwithShaLing,LihongYangandRobinD.P.Zhou.題目11：OnlatticepathsandtheThue-Morsesequence

報(bào)告人：傅士碩教授（重慶大學(xué)）

摘要：InansweringaquestionofBerstel,Lauve,Reutenauer,andSaliola,wepresentacombinatorialargumentbasingonthesymmetryofcertainlatticepathstoexplainthatthediagonalofcertainbivariaterationalfunctioniscongruenttotheThue-Morseseriesmodulo2.題目12：完全對(duì)稱多項(xiàng)式零點(diǎn)的新下界

報(bào)告人：張俊教授（首都師范大學(xué)）

摘要：在報(bào)告中，我們介紹最新的關(guān)于完全對(duì)稱多項(xiàng)式零點(diǎn)個(gè)數(shù)的下界，該下界大大改進(jìn)了已有的下界。該工作是與萬(wàn)大慶教授合作。題目13：Furtherq-supercongruencesfromatransformationofRahman

報(bào)告人：郭軍偉教授（淮陰師范學(xué)院）

摘要：EmployingaquadratictransformationformulaofRahmanandthemethodof`creativemicroscoping'(introducedbytheauthorandZudilinin2019),weprovidesomenewq-supercongruencesfortruncatedbasichypergeometricseries.Inparticular,weconfirmtworecentconjecturesofLiuandWang.Wealsoproposesomerelatedconjecturesonsupercongruencesandq-supercongruences.題目14：OnaconjectureofTokushigeforcross-t-intersectingfamilies

報(bào)告人：張華軍教授（紹興文理學(xué)院）

摘要：TwofamiliesofsetsAandBarecalledcross-t-intersectingifA∩B≥tforallA∈A,B∈B.Inthistalk,wewillprovethatforallk≥t≥3andn≥t+1k-t+1,ifA,B?nkarecross-t-intersecting,then題目15：ModularityofNahmSumsfortheTadpoleDiagram

報(bào)告人：王六權(quán)教授（武漢大學(xué)）

摘要：WeproveRogers-RamanujantypeidentitiesfortheNahmsumsassociatedwiththetadpoleCartanmatrixofrank3.Theseidentitiesrevealthemodularityofthesesums,andtherebyweconfirmaconjectureofCalinescu,MilasandPenninthiscase.WeshowthattheseNahmsumstogetherwithsomeshiftedsumscanbecombinedintoavector-valuedmodularfunctiononthefullmodulargroup.Wealsopresentsomeconjecturesforageneralrank.ThistalkisbasedonajointworkwithAntunMilas.題目16：Generalizedq-partialdifferentialequationsforq-3Dhypergeometricpolynomialsandsomeapplications

報(bào)告人：曹健教授（杭州師范大學(xué)）

摘要：Inthistalk,ourinvestigationisfocusingonq-analoguecomplexHermitepolynomials,whichweremotivatedbyIsmailandZhang[Adv.Appl.Math.80(2016),70--92.]and[Trans.Amer.Math.Soc.369(2017),6779--6821.].Wegiveanewpairofq-3DHermitepolynomialsandtheircorrespondingq-partialdifferentialequations.Inaddition,wegeneralizeq,c-derivativeoperatorofZhang[Adv.Appl.Math.