Computing vector partition functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866916474516406272 |
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| author | Milev, Todor |
| author_facet | Milev, Todor |
| contents | A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors $Δ$. We present a new algorithm for computing closed-form formulas for vector partition functions as quasi-polynomials over a finite set of pointed polyhedral cones, implemented in the ``calculator'' computer algebra system. We include an exposition of previously known theory of vector partition functions. While our results are not new, our exposition is elementary and self-contained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06894 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing vector partition functions Milev, Todor Representation Theory Combinatorics 17B22, 05E10 A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors $Δ$. We present a new algorithm for computing closed-form formulas for vector partition functions as quasi-polynomials over a finite set of pointed polyhedral cones, implemented in the ``calculator'' computer algebra system. We include an exposition of previously known theory of vector partition functions. While our results are not new, our exposition is elementary and self-contained. |
| title | Computing vector partition functions |
| topic | Representation Theory Combinatorics 17B22, 05E10 |
| url | https://arxiv.org/abs/2302.06894 |