---
res:
  bibo_abstract:
  - 'Motivated by higher vanishing multiplicity generalizations of Alon''s Combinatorial
    Nullstellensatz and its applications, we study the following problem: for fixed
    and large with respect to , what is the minimum possible degree of a polynomial
    with such that has zeroes of multiplicity at least at all points in ? For , a
    classical theorem of Alon and Füredi states that the minimum possible degree of
    such a polynomial equals . In this paper, we solve the problem for all , proving
    that the answer is . As an application, we improve a result of Clifton and Huang
    on configurations of hyperplanes in such that each point in is covered by at least
    hyperplanes, but the point is uncovered. Surprisingly, the proof of our result
    involves Catalan numbers and arguments from enumerative combinatorics.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Lisa
      foaf_name: Sauermann, Lisa
      foaf_surname: Sauermann
  - foaf_Person:
      foaf_givenName: Yuval
      foaf_name: Wigderson, Yuval
      foaf_surname: Wigderson
      foaf_workInfoHomepage: http://www.librecat.org/personId=2d0023a0-1567-11f0-833d-d5c1e476d4b5
  bibo_doi: 10.1112/jlms.12637
  bibo_issue: '3'
  bibo_volume: 106
  dct_date: 2022^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0024-6107
  - http://id.crossref.org/issn/1469-7750
  dct_language: eng
  dct_publisher: Wiley@
  dct_title: Polynomials that vanish to high order on most of the hypercube@
...