Obstructions to Combinatorial Formulas for Plethysm

Kahle, Thomas; Michalek, Mateusz

Obstructions to Combinatorial Formulas for Plethysm

Dateien

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Datum

2018

Autor:innen

Kahle, Thomas

Michalek, Mateusz

Open Access-Veröffentlichung

Open Access Gold

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen 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

Zusammenfassung

Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm. We demonstrate, on the examples of S³(S^k) and S^k(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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Representation theory, Plethysm, Ehrhart quasi-polynomial, Kronecker coefficients, Lattice point counting

Zitieren

ISO 690

KAHLE, 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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