M. J. Loquias

activity

20102026

most citedThe coincidence problem for shifted lattices and crystallographic point packings

6 citations · 27 across the 18 of their papers we have counts for

collaborators

18 papers

math.NT2026

A Matrix Analogue of Rational Number Systems

Anjelo Gabriel R. Cruz, Manuel Joseph C. Loquias

Let $P, Q \in Z^{d \times d}$ be invertible coprime matrices such that all the eigenvalues of $Q^{- 1} P$ have modulus greater than 1, and $Z^{d} [Q^{- 1} P]$ be the small…

math.NT2025

Addition Automata and Attractors of Digit Systems Corresponding to Expanding Rational Matrices

Anjelo Gabriel R. Cruz, Manuel Joseph C. Loquias, Jörg M. Thuswaldner

Let $A$ be an expanding $2 \times 2$ matrix with rational entries and $Z^{2} [A]$ be the smallest $A$ -invariant $Z$ -module containing $Z^{2}$ . Let $\mathcal{D…

math.CO2023★ 1 cited

Perfect precise colorings of plane semiregular tilings

Manuel Joseph C. Loquias, Rovin B. Santos

A coloring of a planar semiregular tiling $T$ is an assignment of a unique color to each tile of $T$ . If $G$ is the symmetry group of $T$ , we say that…

math.CO2021

Multiple contractions of permutation arrays

Carmen Amarra, Dom Vito A. Briones, Manuel Joseph C. Loquias

Given a permutation $σ$ on $n$ symbols ${0, 1, \dots, n - 1}$ and an integer $1 \leq m \leq n - 1$ , the $m$ th contraction of $σ$ is the permutation $σ^{CT^{m}}$ on $n - m$ symbols…

math.MG2020

Similarity Isometries of Point Packings

Jeanine Concepcion H. Arias, Manuel Joseph C. Loquias

A linear isometry $R$ of $R^{d}$ is called a similarity isometry of a lattice $Γ \subseteq R^{d}$ if there exists a positive real number $β$ such that $β R Γ$ is a subla…

cs.RO2019★ 1 cited

Inverse Kinematics of Some General 6R/P Manipulators

Jose Capco, Manuel Joseph C. Loquias, Saraleen Mae M. Manongsong +1

We develop an algorithm that solves the inverse kinematics of general serial 2RP3R, 2R2P2R, 3RP2R and 6R manipulators based on the HuPf algorithm. We identify the workspaces of the…

math.CO2018

Fundamental domains for rhombic lattices with dihedral symmetry of order 8

Joseph Ray Clarence G. Damasco, Dirk Frettlöh, Manuel Joseph C. Loquias

We show by construction that every rhombic lattice $Γ$ in $R^{2}$ has a fundamental domain whose symmetry group contains the point group of $Γ$ as a subgroup of index $2$ .…

math.MG2016

Color groups of colorings of $N$ -planar modules

Manuel Joseph C. Loquias, Lilibeth D. Valdez, Ma. Lailani B. Walo

A submodule of a $Z$ -module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a $\mathbb…

math.NT2015★ 1 cited

Rational digit systems over finite fields and Christol's Theorem

Manuel Joseph C. Loquias, Mohamed Mkaouar, Klaus Scheicher +1

Let $P, Q \in F_{q} [X] ∖ {0}$ be two coprime polynomials over the finite field $F_{q}$ with $deg P > deg Q$ . We represent each…

math.MG2015

Coincidence indices of sublattices and coincidences of colorings

Manuel Joseph C. Loquias, Peter Zeiner

Even though a lattice and its sublattices have the same group of coincidence isometries, the coincidence index of a coincidence isometry with respect to a lattice $Λ_{1}$ and to a su…

math.MG2015

Symmetries and color symmetries of a family of tilings with a singular point

Imogene F. Evidente, Rene P. Felix, Manuel Joseph C. Loquias

We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetric…

math.MG2013★ 1 cited

Coincidences of a shifted hexagonal lattice and the hexagonal packing

Jeanine Concepcion H. Arias, Evelyn D. Gabinete, Manuel Joseph C. Loquias

A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices (CSLs) and coincidence site modules (CSMs), respectively. Rec…

math.CO2013★ 1 cited

Highly symmetric fundamental domains for lattices in R^2 and R^3

Joseph Ray Clarence G. Damasco, Dirk Frettlöh, Manuel Joseph C. Loquias

It is shown that most lattices $Γ$ in $R^{2}$ and $R^{3}$ possess a fundamental domain $F$ for the action of $Γ$ on $R^{2}$ , respectively $R^{3}$ , havin…

math.CO2013★ 3 cited

Dually weighted Stirling-type sequences

Roberto B. Corcino, Ken Joffaniel M. Gonzales, Manuel Joseph C. Loquias +1

We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequenc…

math.MG2013★ 6 cited

The coincidence problem for shifted lattices and crystallographic point packings

Manuel Joseph C. Loquias, Peter Zeiner

A coincidence site lattice is a sublattice formed by the intersection of a lattice $Γ$ in $R^{d}$ with the image of $Γ$ under a linear isometry. Such a linear isometry is re…

math.MG2010★ 3 cited

Colourings of lattices and coincidence site lattices

Manuel Joseph C. Loquias, Peter Zeiner

The relationship between the coincidence indices of a lattice $Γ_{1}$ and a sublattice $Γ_{2}$ of $Γ_{1}$ is examined via the colouring of $Γ_{1}$ that is obtained by assigning a unique co…

math.CO2010★ 5 cited

Enumerating and identifying semiperfect colorings of symmetrical patterns

Rene P. Felix, Manuel Joseph C. Loquias

If $G$ is the symmetry group of an uncolored pattern then a coloring of the pattern is semiperfect if the associated color group $H$ is a subgroup of $G$ of index 2. We give result…

math.MG2010★ 5 cited

Coincidence isometries of a shifted square lattice

Manuel Joseph C. Loquias, Peter Zeiner

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the c…

A Matrix Analogue of Rational Number Systems

Addition Automata and Attractors of Digit Systems Corresponding to Expanding Rational Matrices

Perfect precise colorings of plane semiregular tilings

Multiple contractions of permutation arrays

Similarity Isometries of Point Packings

Inverse Kinematics of Some General 6R/P Manipulators

Fundamental domains for rhombic lattices with dihedral symmetry of order 8

Color groups of colorings of N-planar modules

Rational digit systems over finite fields and Christol's Theorem

Coincidence indices of sublattices and coincidences of colorings

Symmetries and color symmetries of a family of tilings with a singular point

Coincidences of a shifted hexagonal lattice and the hexagonal packing

Highly symmetric fundamental domains for lattices in R^2 and R^3

Dually weighted Stirling-type sequences

The coincidence problem for shifted lattices and crystallographic point packings

Colourings of lattices and coincidence site lattices

Enumerating and identifying semiperfect colorings of symmetrical patterns

Coincidence isometries of a shifted square lattice

Color groups of colorings of $N$ -planar modules