arXiv subjects

Paul Tricot

Publications and source records attributed to Paul Tricot.

3 recordsLinked to original sources

arXiv2026

Biangular lines with angles arccos(1/5) and arccos(3/5)

The largest known biangular lines systems in dimension 7 through 20 are due to Ganzhinov and Szöllősi, and the lines make angles $\arccos(\frac{1}{5})$ and $\arccos(\frac{3}{5})$. They are constructed by making use of the nice connection with integral lattices. We explore further the connection between biangular lines and integral lattices to classify the largest biangular line systems with these angles, in dimension 7 through 10. We also give a new biangular line system in dimension 15, that matches the size of the largest known in this dimension.

math.AG↗

arXiv2024

On $3$-designs from $PGL(2,q)$

The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,λ)$ design. We find the parameters of the designs formed by the orbit of a block of the form $\langle θ^r \rangle$ or $\langle θ^r \rangle \cup \{ 0\}$, where $θ$ is a primitive element of $GF(q)$.

math.CO↗

arXiv2024

Symmetric Perfect $2$-colorings on $J(10,3)$

We study perfect $2$-coloring of the Johnson graphs $J(n,3)$ associated with the third largest eigenvalue and symmetric quotient matrix, which exists only when $n \in \{6, 10\}$. We survey the known constructions in the case $n=6$, give a new construction for the two known perfect $2$-colorings in the case $n=10$, and prove that these are the only possible ones.

math.CO↗