Author

Shouda Wang

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Preprint Oct 2026

The maximum number of Hamiltonian cycles in tournaments

Let $C(n)$ denote the maximum number of directed Hamiltonian cycles in a tournament on $n$ vertices. We prove that, as $n\to\infty$, $$ C(n) = \left(\frac{\cosh 1}{\cos 1}\pm o(1)\right)\frac{(n-1)!}{2^n}. $$ The bound is asymptotically attained by the regular tournament with vertices $\mathbb Z/n\mathbb Z$ where $(i,j...

Alexander Divoux, Shouda Wang · 0 citations

Preprint Oct 2026

Higher-order Godbersen inequality and a characterization of simplices via the face lattice

We settle the long-standing Godbersen conjecture that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized precisely by simplices. For the proof, we establish a new characterization of simplices by a natural incidence relation on the face lattice. Moreover, we est...

Filip Fryš, Jan Kotrbatý, Mohamed A. Mouamine et al. · 1 citation

Preprint Sep 2026

The B\'ezout inequality for mixed volumes characterizes simplices

We prove that the B\'ezout inequality for mixed volumes characterizes simplices among full dimensional convex bodies in every dimension, resolving a conjecture of Soprunov and Zvavitch. We give two separate proofs of the conjecture. Along the way, we also prove characterizations of simplices in terms of longest chords...

Dylan Langharst, Shouda Wang · 0 citations