3 citations · 7 across the 9 of their papers we have counts for
11 papers
The Wang--Sun Sum over Affine Derangements
Octavio A. Agust\'ın Aquino
Let be even, let be a primitive -th root of unity, and let be the set of derangements in the affine group . We evaluat…
Cyclic Sieving for Strong Dichotomy Enumeration
Octavio A. Agustín-Aquino
Agustín-Aquino solved, in terms of the table of marks of $\Aff(\mathbb{Z}/2k\mathbb{Z})$, the problem of enumerating the classes of bicolour self-complementary and rigid patterns i…
Exploring Exotic Counterpoint Compositions
Octavio A. Agustín-Aquino, Jeffery Liu, Guerino Mazzola
In this paper, first musical compositions are presented, which are created using the mathematical counterpoint theory of Guerino Mazzola and his collaborators. These compositions a…
Musicological, computational and conceptual aspects of first-species counterpoint theory
Juan Sebastián Arias-Valero, Octavio Alberto Agustín-Aquino, Emilio Lluis-Puebla
We re-create the essential results of a 1989 unpublished article by Mazzola and Muzzulini that contains musicological aspects of a first-species counterpoint model. We include a su…
A Categorical Generalization of Counterpoint
Octavio A. Agustín-Aquino, Juan Sebastián Arias, Enrique Ruiz Hernández
We extend Mazzola's counterpoint model using category theory, generalizing from the category to an arbitrary topos other than . This generalization sug…
Modulation in Tetradic Harmony and its Role in Jazz
Octavio A. Agustín-Aquino, Guerino Mazzola
After a quick exposition of Mazzola's quantum modulation model for the so-called triadic interpretation of the major scale within the equal temperament, we study the model for the…
Archimedes' quadrature of the parabola and minimal covers
Octavio A. Agustín-Aquino
The generalization of Archimedes strategy to obtain the area of a parabolic segment leads to combinatorial formulas involving minimal covers of sets. These, in turn, are conjectura…
Extended counterpoint symmetries and continuous counterpoint
Octavio A. Agustín-Aquino
A counterpoint theory for the whole continuum of the octave is obtained from Mazzola's model via extended counterpoint symmetries, and some of its properties are discussed.
Enumeration of strong dichotomy patterns
Octavio A. Agustín-Aquino
We apply the version of Pólya-Redfield theory obtained by White to count patterns with a given automorphism group to the enumeration of strong dichotomy patterns, that is, we count…
A note on a sumset in
Octavio A. Agustín-Aquino
Let and be additive sets of , where has cardinality and with . In this note some bounds for the c…
Prime injections and quasipolarities
Octavio Alberto Agustín-Aquino
Let be a prime number. Consider the injection \[ ι:\mathbb{Z}/n\mathbb{Z}\to\mathbb{Z}/pn\mathbb{Z}:x\mapsto px, \] and the elements $e^{u}.v:=(u,v)\in \mathbb{Z}/n\mathbb{Z}\r…