Zobrazeno 1 - 10
of 448
pro vyhledávání: '"O'NEILL, CHRISTOPHER"'
Autor:
Chapman, Spencer, Dugan, Eli B., Gaskari, Shadi, Lycan, Emi, De La Cruz, Sarah Mendoza, O'Neill, Christopher, Ponomarenko, Vadim
A factorization of an element $x$ in a monoid $(M, \cdot)$ is an expression of the form $x = u_1^{z_1} \cdots u_k^{z_k}$ for irreducible elements $u_1, \ldots, u_k \in M$, and the length of such a factorization is $z_1 + \cdots + z_k$. We introduce t
Externí odkaz:
http://arxiv.org/abs/2411.17010
We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound (the conduc
Externí odkaz:
http://arxiv.org/abs/2407.15571
Each numerical semigroup $S$ with smallest positive element $m$ corresponds to an integer point in a polyhedral cone $C_m$, known as the Kunz cone. The faces of $C_m$ form a stratification of numerical semigroups that has been shown to respect a numb
Externí odkaz:
http://arxiv.org/abs/2405.01700
Autor:
Landeros, Miguel, O'Neill, Christopher, Pelayo, Roberto, Peña, Karina, Ren, James, Wissman, Brian
The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. Garc\'ia-S\'anchez and Leamer showed that a special case of this conjecture concerning numerical semigroup rings $\Bbbk[\Gamma]$ can be answered in the affirmative
Externí odkaz:
http://arxiv.org/abs/2404.12519
Fix $t\in [1,\infty]$. Let $S$ be an atomic commutative semigroup and, for all $x\in S$, let $\mathscr{L}_t(S):=\{\|f\|_t:f\in Z(x)\}$ be the "$t$-length set" of $x$ (using the standard $l_p$-space definition of $\|\cdot\|_t$). The $t$-Delta set of $
Externí odkaz:
http://arxiv.org/abs/2404.02310
A numerical semigroup $S$ is an additively-closed set of non-negative integers, and a factorization of an element $n$ of $S$ is an expression of $n$ as a sum of generators of $S$. It is known that for a given numerical semigroup $S$, the number of fa
Externí odkaz:
http://arxiv.org/abs/2401.06912
A numerical semigroup is a cofinite subset of $\mathbb Z_{\ge 0}$ containing $0$ and closed under addition. Each numerical semigroup $S$ with smallest positive element $m$ corresponds to an integer point in the Kunz cone $\mathcal C_m \subseteq \math
Externí odkaz:
http://arxiv.org/abs/2401.06025
Autor:
Moskowitz, Gilad, O'Neill, Christopher
For sufficiently nice families of semigroups and monoids, the structure theorem for sets of length states that the length set of any sufficiently large element is an arithmetic sequence with some values omitted near the ends. In this paper, we prove
Externí odkaz:
http://arxiv.org/abs/2311.05786
Consider the set $M_{a,b} = \{n \in \mathbb Z_{\ge 1} : n \equiv a \bmod b\} \cup \{1\}$ for $a, b \in \mathbb Z_{\ge 1}$. If $a^2 \equiv a \bmod b$, then $M_{a,b}$ is closed under multiplication and known as an arithmetic congruence monoid (ACM). A
Externí odkaz:
http://arxiv.org/abs/2310.07924
Numerical semigroups with multiplicity $m$ are parameterized by integer points in a polyhedral cone $C_m$, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall structure is iden
Externí odkaz:
http://arxiv.org/abs/2310.03612