Thomas Fallon

activity

20192023

most citedThe Fuglede Conjecture holds in $\F_p^3$ for p=5,7

6 citations · 9 across the 3 of their papers we have counts for

collaborators

3 papers

math.CA2023★ 1 cited

Spectral Tile Direction in the Group $Z_{p^{2}} \times Z_{q^{2}} \times Z_{r}$

Thomas Fallon, Gergely Kiss, Azita Mayeli +1

Let $p$ , $q$ , and $r$ be distinct primes such that $p^{2} q^{2} < r$ . We prove that every spectral set in the cyclic group $Z_{p^{2} q^{2} r}$ is a tile. Since the reverse direction is…

math.CA2021★ 2 cited

Spectral sets and tiles in $Z_{p}^{2} \times Z_{q}^{2}$

Thomas Fallon, Gergely Kiss, Gábor Somlai

In this paper we study Fuglede's conjecture on the direct product of two cyclic groups. After collecting the known results we prove that Fuglede's conjecture holds on $\mathbb{Z}_{…

math.CA2019★ 6 cited

The Fuglede Conjecture holds in $\F_p^3$ for p=5,7

Thomas Fallon, Azita Mayeli, Dominick Villano

For p=5,7, we show that a subset $E \subset \F_p^3$ is spectral if and only if E tiles $\F_p^3$ by translation. Additionally, we give an alternate proof that the conjecture hol…

Spectral Tile Direction in the Group Zp2​×Zq2​×Zr​

Spectral sets and tiles in Zp2​×Zq2​

The Fuglede Conjecture holds in \(\F_p^3\) for p=5,7

Spectral Tile Direction in the Group $Z_{p^{2}} \times Z_{q^{2}} \times Z_{r}$

Spectral sets and tiles in $Z_{p}^{2} \times Z_{q}^{2}$