Tittle: Locally Semi-Equitable Colourings of Balanced Incomplete Block Designs

Abstract: We study $\ell$-colourings of $(v,k,\lambda)$-BIBDs (balanced incomplete block designs) where, within each block, one colour is absent and each of the $\ell-1$ other colours appears exactly $\frac{k}{\ell-1}$ times. We call such colourings $0$-ULSE, short for uniform 0-locally semi-equitable. We establish several necessary conditions for $0$-ULSE colourings to exist and constructions for BIBDs that admit $0$-ULSE colourings. Using our constructions, we provide new necessary conditions for the existence of Hadamard matrices, affine planes, and twin prime powers. We end the talk with many directions for further research.

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Location: Online

Date and Time: Wednesday, Sept. 2 at 01:00 PM - 04:00 PM (NDT)

For more information: https://mun.webex.com/mun/j.php?MTID=mf9318800e23d6dd92e207b30a7292c7a

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