A short proof of MacLane's planarity theorem

This note gives a short and elementary proof of MacLane's theorem on the embedding of graphs in a 2-sphere

Observation of Electroweak Production of a Same-Sign W Boson Pair in Association with Two Jets in pp Collisions root s=13 TeV with the ATLAS Detector

This Letter presents the observation and measurement of electroweak production of a same-sign W boson pair in association with two jets using 36.1     fb − 1 of proton-proton collision data recorded at a center-of-mass energy of √ s = 13     TeV by the ATLAS detector at the Large Hadron Collider. The analysis is performed in the detector fiducial phase-space region, defined by the presence of two same-sign leptons, electron or muon, and at least two jets with a large invariant mass and rapidity difference. A total of 122 candidate events are observed for a background expectation of 69 ± 7 events, corresponding to an observed signal significance of 6.5 standard deviations. The measured fiducial signal cross section is σ fid = 2.89 + 0.51 − 0.48 ( stat ) + 0.29 − 0.28 ( syst )     fb