SwePub
Sök i SwePub databas

  Extended search

Träfflista för sökning "WFRF:(Jochemko Katharina) srt2:(2018)"

Search: WFRF:(Jochemko Katharina) > (2018)

  • Result 1-2 of 2
Sort/group result
   
EnumerationReferenceCoverFind
1.
  • Berg, S., et al. (author)
  • Ehrhart tensor polynomials
  • 2018
  • In: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 539, s. 72-93
  • Journal article (peer-reviewed)abstract
    • The notion of Ehrhart tensor polynomials, a natural generalization of the Ehrhart polynomial of a lattice polytope, was recently introduced by Ludwig and Silverstein. We initiate a study of their coefficients. In the vector and matrix cases, we give Pick-type formulas in terms of triangulations of a lattice polygon. As our main tool, we introduce hr-tensor polynomials, extending the notion of the Ehrhart h⁎-polynomial, and, for matrices, investigate their coefficients for positive semidefiniteness. In contrast to the usual h⁎-polynomial, the coefficients are in general not monotone with respect to inclusion. Nevertheless, we are able to prove positive semidefiniteness in dimension two. Based on computational results, we conjecture positive semidefiniteness of the coefficients in higher dimensions. Furthermore, we generalize Hibi's palindromic theorem for reflexive polytopes to hr-tensor polynomials and discuss possible future research directions.
  •  
2.
  • Jochemko, Katharina, et al. (author)
  • Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem
  • 2018
  • In: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 20:9, s. 2181-2208
  • Journal article (peer-reviewed)abstract
    • We introduce the notion of combinatorial positivity of translation-invariant valuations on convex polytopes that extends the nonnegativity of Ehrhart h∗-vectors. We give a surprisingly simple characterization of combinatorially positive valuations that implies Stanley’s nonnegativity and monotonicity of h∗-vectors and generalizes work of Beck et al. (2010) from solid-angle polynomials to all translation-invariant simple valuations. For general polytopes, this yields a new characterization of the volume as the unique combinatorially positive valuation up to scaling. For lattice polytopes our results extend work of Betke–Kneser (1985) and give a discrete Hadwiger theorem: There is essentially a unique combinatorially-positive basis for the space of lattice-invariant valuations. As byproducts, we prove a multivariate Ehrhart–Macdonald reciprocity and we show universality of weight valuations studied in Beck et al. (2010).
  •  
Skapa referenser, mejla, bekava och länka
  • Result 1-2 of 2
Type of publication
journal article (2)
Type of content
peer-reviewed (2)
Author/Editor
Jochemko, Katharina (2)
Berg, S. (1)
Silverstein, L. (1)
Sanyal, R. (1)
University
Royal Institute of Technology (2)
Language
English (2)
Research subject (UKÄ/SCB)
Natural sciences (2)
Year
2018 (2)Undo refine

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.

 
pil uppåt Close

Copy and save the link in order to return to this view