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Gặp gỡ Toán học 2025 - Hội thảo Khoa học các nhà nghiên cứu trẻ"
Lectures on selected areas in Pure Mathematics
Hội nghị toàn quốc lần thứ VII “Xác suất - Thống kê: Nghiên cứu, ứng dụng và giảng dạy”
Xuất bản mới
Discrepancy of hypergraph pairs
Người báo cáo: Trần Mạnh Tuấn
Speaker: Prof. Tuan Tran, University of Science and Technology of China
Thời gian: 14h Thứ 5, ngày 08/05/2025
Địa điểm: Phòng 507 nhà A6
Link online Zoom: https://us06web.zoom.us/j/89134062450?pwd=io7luDnBIrkYTZLXvCuwAKdJPokluC.1
Meeting ID: 891 3406 2450
Passcode: 123456
Tóm tắt: The discrepancy of a pair of hypergraphs, introduced by Bollobás and Scott (2010), measures how uniformly and independently their edges are distributed. Building on results by Erdős and Spencer, Bollobás and Scott conjectured that any pair of k-uniform hypergraphs of moderate density should have a large discrepancy. While they confirmed this for k = 2, they later found a counterexample for k = 3.
In our paper, we extend their results by providing a counterexample for all k > 2. We also show that for k = 3, 4, ..., 14, any collection of three k-uniform hypergraphs of moderate density always contains a pair with large discrepancy.
This work is based on joint research with Diep Luong and Yang Dilong.