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Factorization length distribution for affine semigroups II: asymptotic behavior for numerical semigroups with arbitrarily many generators

Autor: Garcia, Stephan Ramon, Omar, Mohamed, O'Neill, Christopher, Yih, Samuel

Publikováno v: J. Combin. Theory Ser. A, 178 (2021), 105358

For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational representations, for all major factorization length statistics. This in

Externí odkaz: http://arxiv.org/abs/1911.04575

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Squarefree divisor complexes of certain numerical semigroup elements

Autor: Autry, Jackson, Graves, Paige, Loucks, Jessie, O'Neill, Christopher, Ponomarenko, Vadim, Yih, Samuel

Publikováno v: Involve 14 (2021) 1-9

A numerical semigroup $S$ is an additive subsemigroup of the non-negative integers with finite complement, and the squarefree divisor complex of an element $m \in S$ is a simplicial complex $\Delta_m$ that arises in the study of multigraded Betti num

Externí odkaz: http://arxiv.org/abs/1804.06632

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Factorization length distribution for affine semigroups I: numerical semigroups with three generators

Autor: Garcia, Stephan Ramon, O'Neill, Christopher, Yih, Samuel

Publikováno v: European J. Combinatorics 78 (2019), 190-204

Most factorization invariants in the literature extract extremal factorization behavior, such as the maximum and minimum factorization lengths. Invariants of intermediate size, such as the mean, median, and mode factorization lengths are more subtle.

Externí odkaz: http://arxiv.org/abs/1804.05135

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Supercharacters and the discrete Fourier, cosine, and sine transforms

Autor: Garcia, Stephan Ramon, Yih, Samuel

Publikováno v: Comm. Algebra 46 (2018), no. 9, 3745-3765

Using supercharacter theory, we identify the matrices that are diagonalized by the discrete cosine and discrete sine transforms, respectively. Our method affords a combinatorial interpretation for the matrix entries.
Comment: 21 pages; to appear

Externí odkaz: http://arxiv.org/abs/1702.02689

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