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Настоящая книга посвящена различным аспектам задачи о системах общих представителей в комбинаторике. Рассказывается о многочисленных приложениях в комбинаторной геометрии, геометрии чисел, математической статистике и др. Книга написана по лекциям, которые ее автор читал в 2007 году на школе «Современная математика» в Дубне. Поэтому материал в ней изложен так, чтобы б'ольшая его часть оказалась доступной первокурсникам. Однако материала много, и в конечном счете в книге возникает весьма нетривиальная техника, в том числе вероятностная. Книга будет интересна всем, кто интересуется современной комбинаторикой и ее приложениями.
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