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A counterexample to a conjecture of A. R. Miller
Gabriel Navarro, Benjamin Sambale
https://arxiv.org/abs/2510.10734 https://arxiv.org/pdf/2510.10734…

A counterexample to a conjecture of A. R. Miller
Let $χ$ be an irreducible character of a finite group $G$. A. R. Miller conjectured that the proportion of elements $g\in G$ such that $χ(g)$ is zero or a root of unity is at least 1/2. We construct a character of a perfect group of order 69120 such that this proportion is 511/1152.

On Kotzig's conjecture in random graphs
Stefan Glock, Amedeo Sgueglia
https://arxiv.org/abs/2510.01949 https://arxiv.org/pdf/2510.01949

On Kotzig's conjecture in random graphs
In 1963, Anton Kotzig famously conjectured that $K_{n}$, the complete graph of order $n$, where $n$ is even, can be decomposed into $n-1$ perfect matchings such that every pair of these matchings forms a Hamilton cycle. The problem is still wide open and here we consider a variant of it for the binomial random graph $G(n,p)$. We prove that, for every fixed $k$, there exists a constant $C=C(k)$ such that, when $p\ge \frac{C \log n}{n}$, with high probability, $G(n,p)$ contains $k$ edge-disjoint …

Irrationality as a mean of regularization in Bayesian Persuasion
Romain Duboscq (IMT, INSA Toulouse), Fr\'ed\'eric de Gournay (IMT, INSA Toulouse)
https://arxiv.org/abs/2510.01759

Irrationality as a mean of regularization in Bayesian Persuasion
We study a regularized variant of the Bayesian Persuasion problem, where the receiver's decision process includes a divergence-based penalty that accounts for deviations from perfect rationality. This modification smooths the underlying optimization landscape and mitigates key theoretical issues, such as measurability and ill-posedness, commonly encountered in the classical formulation. It also enables the use of scalable second-order optimization methods to compute numerically the optimal sign…