Hilbert Bases and Lecture Hall Partitions
| Autor: | McCabe Olsen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
0102 computer and information sciences
Characterization (mathematics) Commutative Algebra (math.AC) 01 natural sciences Combinatorics Set (abstract data type) symbols.namesake FOS: Mathematics Mathematics - Combinatorics Number Theory (math.NT) 0101 mathematics Mathematics Algebra and Number Theory Mathematics - Number Theory 010102 general mathematics Condensed Matter::Mesoscopic Systems and Quantum Hall Effect Physics::Classical Physics Mathematics - Commutative Algebra 05A17 05A19 11P21 13A02 13H10 13P99 52B11 Lecture hall Number theory 010201 computation theory & mathematics Fourier analysis Physics::Space Physics symbols Generating set of a group Combinatorics (math.CO) |
| Popis: | In the interest of finding the minimum additive generating set for the set of $\boldsymbol{s}$-lecture hall partitions, we compute the Hilbert bases for the $\boldsymbol{s}$-lecture hall cones in certain cases. In particular, we compute the Hilbert bases for two well-studied families of sequences, namely the $1\mod k$ sequences and the $\ell$-sequences. Additionally, we provide a characterization of the Hilbert bases for $\boldsymbol{u}$-generated Gorenstein $\boldsymbol{s}$-lecture hall cones in low dimensions. Final Version. To appear in Ramanujan J |
| Databáze: | OpenAIRE |
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