| Monday 25 November 2024 | |
| Events for day: Wednesday 23 October 2024 |
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Proof of a Conjecture of Cavenagh, Hamalainen, Lefevre, and Stones School MATHEMATICS An $r imes r$ {it $lambda$-Latin square} ({it rectangle}, respectively) is an $r imes r$ array in which each cell contains a multiset of $lambda$ elements from the set ${1,dots,r}$ of symbols such that each symbol occurs exactly $lambda$ times (at most $lambda$ times, respectively) in each row and column. Cavenagh, Hämäläinen, Lefevre, and Stones asked for conditions that ensure a simple λ-Latin rectangle can be extended to a simple λ-Latin square. We solve this problem in a more general setting by allowing the number of occurrences of each symbol to be prescribed. Cavenagh et al. also conjectured that for each r,λ there exi ... 16:00 - 17:00 Mathematics Colloquium Secret Sharing Schemes School MATHEMATICS Secret sharing is a cryptographic concept introduced in 1979. In a secret sharing scheme, a secret is distributed among a set of participants by giving each one a share. The shares are computed by applying a public rule to the secret and some randomness. Only certain pre-specified subsets of participants are qualified to recover the secret, while the secret remains hidden from all other subsets. Secret sharing is significant from both theoretical and practical perspectives. In this talk, I will survey our results from 2018 to 2024 and introduce several open problems. Subscribing the Mathematics Colloquium mailing list: ... |