What Do You Know About Schubert Polynomials?

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  • 1/10 Questions

    Schubert polynomials are generalizations of Schur polynomials that represent which of these?

    • Trihomology classes
    • Dihomology classes
    • Homology classes
    • Teramology classes
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About This Quiz

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.

What Do You Know About Schubert Polynomials? - Quiz

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  • 2. 
    Who introduced Schubert polynomials? - ProProfs

    Who introduced Schubert polynomials?

    • Richard and Stanley

    • Lascoux and Schutzenberger

    • Lascoux and Richard

    • Stanley and Hermaine

    Correct Answer
    A. Lascoux and Schutzenberger
    Explanation
    Lascoux and Schutzenberger introduced Schubert polynomials.

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  • 3. 
    Which of these individuals put forth a conjectural rule for their coefficients? - ProProfs

    Which of these individuals put forth a conjectural rule for their coefficients?

    • Sara Billey

    • Richard P. Stanley

    • Sergey Formin

    • Lasoux

    Correct Answer
    A. Richard P. Stanley
    Explanation
    Richard P. Stanley is the correct answer because he is known for his work in algebraic combinatorics and has made significant contributions to the field. In particular, he has put forth a conjectural rule for the coefficients of certain combinatorial polynomials, which suggests a relationship between various combinatorial objects. This conjecture has been influential in the study of combinatorial structures and has led to further research and developments in the field.

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  • 4. 
    In which year was the history of Schubert polynomials described? - ProProfs

    In which year was the history of Schubert polynomials described?

    • 1995

    • 1996

    • 1997

    • 1998

    Correct Answer
    A. 1995
    Explanation
    The history of Schubert polynomials was described in the year 1995.

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  • 5. 
    What do we call the Schubert polynomials that can be seen as a generating function over certain combinatorial objects? - ProProfs

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

    • Pipe dreams or rc-graphs

    • Ripe dreams or rd-graphs

    • Side dreams or 3d-graphs

    • Side dreams or 4s-graphs

    Correct Answer
    A. Pipe dreams or rc-graphs
    Explanation
    Pipe dreams or rc-graphs are called the Schubert polynomials that can be seen as a generating function over certain combinatorial objects.

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  • 6. 
    Fomin, Gelfand, and Postnikov introduced quantum Schubert polynomials in which year?  - ProProfs

    Fomin, Gelfand, and Postnikov introduced quantum Schubert polynomials in which year? 

    • 1997

    • 1996

    • 1995

    • 1994

    Correct Answer
    A. 1997
    Explanation
    Fomin, Gelfand, and Postnikov introduced quantum Schubert polynomials in 1997.

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  • 7. 
    Which of the following does Schubert polynomials have? - ProProfs

    Which of the following does Schubert polynomials have?

    • Negative coefficient

    • Positive coefficient

    • Neutral coefficient

    • The coefficient depends on the value

    Correct Answer
    A. Positive coefficient
    Explanation
    Schubert polynomials have positive coefficients. This means that each term in the polynomial has a positive coefficient, indicating that the polynomial is always positive or non-negative.

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  • 8. 
    Double Schubert polynomials are polynomials in what?   - ProProfs

    Double Schubert polynomials are polynomials in what?  

    • 1 infinite set of variables

    • 2 infinite sets of variables

    • 3 infinite sets of variables

    • 4 infinite set of variables

    • No infinite set of variables

    Correct Answer
    A. 2 infinite sets of variables
    Explanation
    Double Schubert polynomials are polynomials in two infinite sets of variables. These polynomials are used in algebraic geometry and combinatorics to study the intersection theory on Grassmannians and flag varieties. The two infinite sets of variables correspond to the Schubert cells and the opposite Schubert cells, which are important objects in the study of flag varieties. The double Schubert polynomials encode information about the intersection numbers of these cells and have applications in representation theory and algebraic geometry.

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  • 9. 
    Who described the history of Schubert polynomials? - ProProfs

    Who described the history of Schubert polynomials?

    • Lascoux

    • Jockush

    • Sergey

    • Hermaine

    Correct Answer
    A. Lascoux
    Explanation
    Lascoux is the correct answer because they are the one who described the history of Schubert polynomials.

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  • 10. 
    After who are Schubert polynomials named? - ProProfs

    After who are Schubert polynomials named?

    • Hermaine Schubert

    • Hermanne Schubert

    • Herman Schubert

    • Henry Schubert

    Correct Answer
    A. Hermanne Schubert
    Explanation
    Schubert polynomials are named after Hermanne Schubert. The spelling of her name is "Hermanne" and not "Hermaine" or "Herman" or "Henry". Therefore, the correct answer is Hermanne Schubert.

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  • Current Version
  • Dec 06, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Jun 18, 2018
    Quiz Created by
    AdeKoju
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