Matrix factorizations and pentagon maps
P Kassotakis - Proceedings of the Royal Society A, 2023 - royalsocietypublishing.org
We propose a specific class of matrices that participate in factorization problems that turn out
to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or …
to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or …
Idempotent set-theoretical solutions of the pentagon equation
M Mazzotta - Bollettino dell'Unione Matematica Italiana, 2024 - Springer
A set-theoretical solution of the pentagon equation on a non-empty set X is a function s: X×
X→ X× X satisfying the relation s 23 s 13 s 12= s 12 s 23, with s 12= s× id X, s 23= id X× s …
X→ X× X satisfying the relation s 23 s 13 s 12= s 12 s 23, with s 12= s× id X, s 23= id X× s …
Set-theoretical solutions of the Yang–Baxter and pentagon equations on semigroups
Abstract The Yang–Baxter and pentagon equations are two well-known equations of
Mathematical Physic. If S is a set, a map s: S * S → S * S s: S× S→ S× S is said to be a set …
Mathematical Physic. If S is a set, a map s: S * S → S * S s: S× S→ S× S is said to be a set …
A survey on set-theoretical solutions to the pentagon equation
M Mazzotta - arXiv preprint arXiv:2312.16958, 2023 - arxiv.org
A survey on set-theoretical solutions to the pentagon equation Page 1 arXiv:2312.16958v1 [math.QA]
28 Dec 2023 A survey on set-theoretical solutions to the pentagon equation Marzia …
28 Dec 2023 A survey on set-theoretical solutions to the pentagon equation Marzia …
Set-theoretic solutions of the pentagon equation
A set-theoretic solution of the Pentagon Equation on a non-empty set S is a map s: S^ 2 →
S^ 2 s: S 2→ S 2 such that s_ 23 s_ 13 s_ 12= s_ 12 s_ 23 s 23 s 13 s 12= s 12 s 23, where …
S^ 2 s: S 2→ S 2 such that s_ 23 s_ 13 s_ 12= s_ 12 s_ 23 s 23 s 13 s 12= s 12 s 23, where …
On the structure of set-theoretic polygon equations
F Müller-Hoissen - … . Symmetry, Integrability and Geometry: Methods and …, 2024 - emis.de
Polygon equations generalize the prominent pentagon equation in very much the same way
as simplex equations generalize the famous Yang-Baxter equation. In particular, they …
as simplex equations generalize the famous Yang-Baxter equation. In particular, they …
Set-theoretical solutions of the pentagon equation on Clifford semigroups
Given a set-theoretical solution of the pentagon equation s: S× S→ S× S on a set S and
writing s (a, b)=(a· b, θ a (b)), with· a binary operation on S and θ aa map from S into itself, for …
writing s (a, b)=(a· b, θ a (b)), with· a binary operation on S and θ aa map from S into itself, for …
On commutative set-theoretic solutions of the Pentagon Equation
M Castelli - arXiv preprint arXiv:2404.13758, 2024 - arxiv.org
We extend the so-called retract relation given in [6] for involutive set-theoretic solutions of
the Pentagon Equation and we introduce the notion of associated permutation group to …
the Pentagon Equation and we introduce the notion of associated permutation group to …
[PDF][PDF] Set-theoretical solutions to the pentagon equation: a survey
M Mazzotta - Communications in Mathematics, 2024 - cm.episciences.org
arXiv:2312.16958v4 [math.QA] 14 May 2024 Page 1 arXiv:2312.16958v4 [math.QA] 14 May
2024 Communications in Mathematics 33 (2025), no. 3, Paper no. 2 DOI: https://doi.org/10.46298/cm.16958 …
2024 Communications in Mathematics 33 (2025), no. 3, Paper no. 2 DOI: https://doi.org/10.46298/cm.16958 …
On quadrirational pentagon maps
We classify rational solutions of a specific type of the set theoretical version of the pentagon
equation. That is, we find all quadrirational maps $ R:(x, y)\mapsto (u (x, y), v (x, y)), $ where …
equation. That is, we find all quadrirational maps $ R:(x, y)\mapsto (u (x, y), v (x, y)), $ where …