4 problems

Equality conjecture. An $s$-motion planning algorithm for $\operatorname{\mathbb{R}P}^m$ with $\operatorname{secat}(\pi_s)+1$ $s$-local rules can be constructed out of such a map.…

Let $\mathcal{P}_{6,48}$ be the centrally symmetric simplicial $6$-polytope whose antipodal quotient of the boundary gives a triangulation of $\mathbb{R}P^5$. A triangulation is ve…

Assume $m\equiv2^e-1\pmod{2^{e+1}}$ with $e\geq0$, so $e$ is the length of the block of consecutive ones ending the binary expansion of $m$. Let…

Let $\mathbb{R}P^4_{16}$ denote the constructed $16$-vertex triangulation of the real projective $4$-space $\mathbb{R}P^4$. Uniqueness conjecture. $\mathbb{R}P^4_{16}$ is the uniqu…