Obstructions to combinatorial formulas for plethysm

Research output: Contribution to journalArticleScientificpeer-review

Researchers

  • Thomas Kahle
  • Mateusz Michalek

Research units

  • Otto-von-Guericke-Universität Magdeburg
  • Max Planck Inst Math Sci, Max Planck Society
  • Polish Acad Sci, Polish Academy of Sciences, Math Inst

Abstract

Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm. We demonstrate, on the examples of S-3(S-k ) and S-k(S-3 ), 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.

Details

Original languageEnglish
Article numberARTN P1.41
Number of pages9
JournalThe Electronic Journal of Combinatorics
Volume25
Issue number1
Publication statusPublished - 2 Mar 2018
MoE publication typeA1 Journal article-refereed

    Research areas

  • GEOMETRIC COMPLEXITY THEORY, KRONECKER COEFFICIENTS, EQUATIONS

ID: 30273041