What Do You Know About Schubert Polynomials?

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What Do You Know About Schubert Polynomials?

Schubert polynomials are speculations of Schur polynomials that speak to cohomology classes of Schubert cycles in flag or hail assortments. In mathematics, there are many variations, which include double Schubert polynomials, quantum Schubert polynomials, and universal Schubert polynomials. If you'd like to know more about Schubert polynomials, take the short quiz below to assess your knowledge.


Questions and Answers
  • 1. 
    Schubert polynomials are generalizations of Schur polynomials that represent which of these?
    • A. 

      Trihomology classes

    • B. 

      Dihomology classes

    • C. 

      Homology classes

    • D. 

      Teramology classes

  • 2. 
    Who introduced Schubert polynomials?
    • A. 

      Richard and Stanley

    • B. 

      Lascoux and Schutzenberger

    • C. 

      Lascoux and Richard

    • D. 

      Stanley and Hermaine

  • 3. 
    After who are Schubert polynomials named?
    • A. 

      Hermaine Schubert

    • B. 

      Hermanne Schubert

    • C. 

      Herman Schubert

    • D. 

      Henry Schubert

  • 4. 
    Which of the following does Schubert polynomials have?
    • A. 

      Negative coefficient

    • B. 

      Positive coefficient

    • C. 

      Neutral coefficient

    • D. 

      The coefficient depends on the value

  • 5. 
    Double Schubert polynomials are polynomials in what?  
    • A. 

      1 infinite set of variables

    • B. 

      2 infinite sets of variables

    • C. 

      3 infinite sets of variables

    • D. 

      4 infinite set of variables

    • E. 

      No infinite set of variables

  • 6. 
    Which of these individuals put forth a conjectural rule for their coefficients?
    • A. 

      Sara Billey

    • B. 

      Richard P. Stanley

    • C. 

      Sergey Formin

    • D. 

      Lasoux

  • 7. 
    Who described the history of Schubert polynomials?
    • A. 

      Lascoux

    • B. 

      Jockush

    • C. 

      Sergey

    • D. 

      Hermaine

  • 8. 
    In which year was the history of Schubert polynomials described?
    • A. 

      1995

    • B. 

      1996

    • C. 

      1997

    • D. 

      1998

  • 9. 
    What do we call the Schubert polynomials that can be seen as a generating function over certain combinatorial objects?
    • A. 

      Pipe dreams or rc-graphs

    • B. 

      Ripe dreams or rd-graphs

    • C. 

      Side dreams or 3d-graphs

    • D. 

      Side dreams or 4s-graphs

  • 10. 
    Fomin, Gelfand, and Postnikov introduced quantum Schubert polynomials in which year? 
    • A. 

      1997

    • B. 

      1996

    • C. 

      1995

    • D. 

      1994