Obstructions to Combinatorial Formulas for Plethysm

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2018
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Kahle, Thomas
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The Electronic Journal of Combinatorics. International Press. 2018, 25(1), P1.41. ISSN 1097-1440. eISSN 1077-8926. Available under: doi: 10.37236/6597
Zusammenfassung

Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm. We demonstrate, on the examples of S3(Sk) and Sk(S3), that these need not be counting functions of inhomogeneous polytopes of dimension equal to the degree of the quasi-polynomial. It follows that these functions are not, in general, counting functions of lattice points in any scaled convex bodies, even when restricted to single rays. Our results also apply to special rectangular Kronecker coefficients.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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Representation theory, Plethysm, Ehrhart quasi-polynomial, Kronecker coefficients, Lattice point counting
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ISO 690KAHLE, Thomas, Mateusz MICHALEK, 2018. Obstructions to Combinatorial Formulas for Plethysm. In: The Electronic Journal of Combinatorics. International Press. 2018, 25(1), P1.41. ISSN 1097-1440. eISSN 1077-8926. Available under: doi: 10.37236/6597
BibTex
@article{Kahle2018Obstr-53572,
  year={2018},
  doi={10.37236/6597},
  title={Obstructions to Combinatorial Formulas for Plethysm},
  number={1},
  volume={25},
  issn={1097-1440},
  journal={The Electronic Journal of Combinatorics},
  author={Kahle, Thomas and Michalek, Mateusz},
  note={Article Number: P1.41}
}
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