We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWF and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET, ERC and NSRF, European Union; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation, Germany; GSRT and NSRF, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; BRF and RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS (MECTS), Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of America. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide.
ANPCyT, Argentina ; YerPhI, Armenia ; ARC, Australia ; BMWFW, Austria ; FWF, Austria ; ANAS, Azerbaijan ; SSTC, Belarus ; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; NSERC, Canada ; NRC, Canada ; CFI, Canada ; CERN ; CONICYT, Chile ; CAS, China ; MOST, China ; NSFC, China ; COLCIENCIAS, Colombia ; MSMT CR, Czech Republic ; MPO CR, Czech Republic ; VSC CR, Czech Republic ; DNRF, Denmark ; DNSRC, Denmark ; IN2P3-CNRS, CEA-DRF/IRFU, France ; SRNSFG, Georgia ; BMBF, Germany ; HGF, Germany ; MPG, Germany ; GSRT, Greece ; RGC, Hong Kong SAR, China ; ISF, Israel ; Benoziyo Center, Israel ; INFN, Italy ; MEXT, Japan ; JSPS, Japan ; CNRST, Morocco ; NWO, Netherlands ; RCN, Norway ; MNiSW, Poland ; NCN, Poland ; FCT, Portugal ; MNE/IFA, Romania ; MES of Russia, Russian Federation ; NRC KI, Russian Federation ; JINR ; MESTD, Serbia ; MSSR, Slovakia ; ARRS, Slovenia ; MIZS, Slovenia ; DST/NRF, South Africa ; MINECO, Spain ; SRC, Sweden ; Wallenberg Foundation, Sweden ; SERI, Switzerland ; SNSF, Switzerland ; Canton of Bern, Switzerland ; MOST, Taiwan ; TAEK, Turkey ; STFC, United Kingdom ; DOE, United States of America ; NSF, United States of America ; BCKDF, Canada ; CANARIE, Canada ; CRC, Canada ; Compute Canada, Canada ; COST, European Union ; ERC, European Union ; ERDF, European Union ; Horizon 2020, European Union ; Marie Sk lodowska-Curie Actions, European Union ; Investissements d' Avenir Labex and Idex, ANR, France ; DFG, Germany ; AvH Foundation, Germany ; Greek NSRF, Greece ; BSF-NSF, Israel ; GIF, Israel ; CERCA Programme Generalitat de Catalunya, Spain ; Royal Society, United Kingdom ; Leverhulme Trust, United Kingdom ; BMBWF (Austria) ; FWF (Austria) ; FNRS (Belgium) ; FWO (Belgium) ; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) ; Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) ; FAPERGS (Brazil) ; MES (Bulgaria) ; CAS (China) ; MoST (China) ; NSFC (China) ; COLCIENCIAS (Colombia) ; MSES (Croatia) ; CSF (Croatia) ; RPF (Cyprus) ; SENESCYT (Ecuador) ; MoER (Estonia) ; ERC IUT (Estonia) ; ERDF (Estonia) ; Academy of Finland (Finland) ; MEC (Finland) ; HIP (Finland) ; CEA (France) ; CNRS/IN2P3 (France) ; BMBF (Germany) ; DFG (Germany) ; HGF (Germany) ; GSRT (Greece) ; NKFIA (Hungary) ; DAE (India) ; DST (India) ; IPM (Iran) ; SFI (Ireland) ; INFN (Italy) ; MSIP (Republic of Korea) ; NRF (Republic of Korea) ; MES (Latvia) ; LAS (Lithuania) ; MOE (Malaysia) ; UM (Malaysia) ; BUAP (Mexico) ; CINVESTAV (Mexico) ; CONACYT (Mexico) ; LNS (Mexico) ; SEP (Mexico) ; UASLP-FAI (Mexico) ; MOS (Montenegro) ; MBIE (New Zealand) ; PAEC (Pakistan) ; MSHE (Poland) ; NSC (Poland) ; FCT (Portugal) ; JINR (Dubna) ; MON (Russia) ; RosAtom (Russia) ; RAS (Russia) ; RFBR (Russia) ; NRC KI (Russia) ; MESTD (Serbia) ; SEIDI (Spain) ; CPAN (Spain) ; PCTI (Spain) ; FEDER (Spain) ; MOSTR (Sri Lanka) ; MST (Taipei) ; ThEPCenter (Thailand) ; IPST (Thailand) ; STAR (Thailand) ; NSTDA (Thailand) ; TAEK (Turkey) ; NASU (Ukraine) ; SFFR (Ukraine) ; STFC (United Kingdom ; DOE (U.S.A.) ; NSF (U.S.A.) ; Marie-Curie programme ; Horizon 2020 Grant (European Union) ; Leventis Foundation ; A.P. Sloan Foundation ; Alexander von Humboldt Foundation ; Belgian Federal Science Policy Office ; Fonds pour la Formation a la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium) ; Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium) ; F.R.S.-FNRS (Belgium) ; Beijing Municipal Science & Technology Commission ; Ministry of Education, Youth and Sports (MEYS) of the Czech Republic ; Hungarian Academy of Sciences (Hungary) ; New National Excellence Program UNKP (Hungary) ; Council of Science and Industrial Research, India ; HOMING PLUS programme of the Foundation for Polish Science ; European Union, Regional Development Fund ; Mobility Plus programme of the Ministry of Science and Higher Education ; National Science Center (Poland) ; National Priorities Research Program by Qatar National Research Fund ; Programa Estatal de Fomento de la Investigacion Cientfica y Tecnica de Excelencia Maria de Maeztu ; Programa Severo Ochoa del Principado de Asturias ; EU-ESF ; Greek NSRF ; Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University (Thailand) ; Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand) ; Welch Foundation ; Weston Havens Foundation (U.S.A.) ; Canton of Geneva, Switzerland ; Herakleitos programme ; Thales programme ; Aristeia programme ; European Research Council (European Union) ; Horizon 2020 Grant (European Union): 675440 ; FWO (Belgium): 30820817 ; Beijing Municipal Science & Technology Commission: Z181100004218003 ; NKFIA (Hungary): 123842 ; NKFIA (Hungary): 123959 ; NKFIA (Hungary): 124845 ; NKFIA (Hungary): 124850 ; NKFIA (Hungary): 125105 ; National Science Center (Poland): Harmonia 2014/14/M/ST2/00428 ; National Science Center (Poland): Opus 2014/13/B/ST2/02543 ; National Science Center (Poland): 2014/15/B/ST2/03998 ; National Science Center (Poland): 2015/19/B/ST2/02861 ; National Science Center (Poland): Sonata-bis 2012/07/E/ST2/01406 ; Programa Estatal de Fomento de la Investigacion Cientfica y Tecnica de Excelencia Maria de Maeztu: MDM-2015-0509 ; Welch Foundation: C-1845 ; This paper presents the combinations of single-top-quark production cross-section measurements by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at = 7 and 8 TeV corresponding to integrated luminosities of 1.17 to 5.1 fb(-1) at = 7 TeV and 12.2 to 20.3 fb(-1) at = 8 TeV. These combinations are performed per centre-of-mass energy and for each production mode: t-channel, tW, and s-channel. The combined t-channel cross-sections are 67.5 +/- 5.7 pb and 87.7 +/- 5.8 pb at = 7 and 8 TeV respectively. The combined tW cross-sections are 16.3 +/- 4.1 pb and 23.1 +/- 3.6 pb at = 7 and 8 TeV respectively. For the s-channel cross-section, the combination yields 4.9 +/- 1.4 pb at = 8 TeV. The square of the magnitude of the CKM matrix element V-tb multiplied by a form factor f(LV) is determined for each production mode and centre-of-mass energy, using the ratio of the measured cross-section to its theoretical prediction. It is assumed that the top-quark-related CKM matrix elements obey the relation |V-td|, |V-ts| « |V-tb|. All the |f(LV)V(tb)|(2) determinations, extracted from individual ratios at = 7 and 8 TeV, are combined, resulting in |f(LV)V(tb)| = 1.02 +/- 0.04 (meas.) +/- 0.02 (theo.). All combined measurements are consistent with their corresponding Standard Model predictions.