19 citations · 34 across the 11 of their papers we have counts for
12 papers
Reflective numerical semigroups
Caleb M. Shor
We define a reflective numerical semigroup of genus as a numerical semigroup that has a certain reflective symmetry when viewed within as an array with columns…
On residues of rounded shifted fractions with a common numerator
Nicholas Dent, Caleb M. Shor
For any positive integer along with parameters and , we define and investigate -shifted, -offset, floor sequences of length . We find exact and asymptotic formu…
Equidistribution of numerical semigroup gaps modulo
Caleb McKinley Shor
For a positive integer , a finite set of integers is said to be equidistributed modulo if the set contains an equal number of elements in each congruence class modulo . I…
On Free Numerical Semigroups and the Construction of Minimal Telescopic Sequences
Caleb M. Shor
A free numerical semigroup is a submonoid of the non-negative integers with finite complement that is additively generated by the terms in a telescopic sequence with gcd 1. However…
Characterizations of numerical semigroup complements via Apéry sets
T. Alden Gassert, Caleb McKinley Shor
In this paper, we generalize the work of Tuenter to give an identity which completely characterizes the complement of a numerical semigroup in terms of its Apéry sets. Using this r…
On Sylvester sums of compound sequence semigroup complements
Thomas A. Gassert, Caleb M. Shor
In this paper, we consider the set of natural numbers which are not in the numerical semigroup generated by a compound sequence . We generalize a result of Tuen…
Higher-order Weierstrass weights of branch points on superelliptic curves
Caleb McKinley Shor
In this paper we consider the problem of calculating the higher-order Weierstrass weight of the branch points of a superelliptic curve . For any , we give an exact formula…
Weierstrass points of superelliptic curves
T. Shaska, C. Shor
In this lecture we give a brief introduction to Weierstrass points of curves and computational aspects of -Weierstrass points on superelliptic curves.
On Jacobians of curves with superelliptic components
Lubjana Beshaj, Tony Shaska, Caleb Shor
We investigate the decomposition of Jacobians of superelliptic curves based on their automorphisms. For curve with equation we provide an necessary and sufficient cond…
Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields
Tony Shaska, Caleb Shor
In this paper we continue the study of codes over imaginary quadratic fields and their weight enumerators and theta functions. We present new examples of non-equivalent codes over…
The 2-Weierstrass points of genus 3 hyperelliptic curves with extra automorphisms
T. Shaska, C. Shor
For each group , \, which acts as a full automorphism group on a genus 3 hyperelliptic curve, we determine the family of curves which have 2-Weierstrass points. Such…
Codes over rings of size and lattices over imaginary quadratic fields
T. Shaska, C. Shor, G. Wijesiri
Let be a square-free integer congruent to 3 mod 4 and the ring of integers of the imaginary quadratic field . Codes over rings d…