How Long to Read Existence of Unimodular Triangulations–Positive Results
By Christian Haase
How Long Does it Take to Read Existence of Unimodular Triangulations–Positive Results?
It takes the average reader 1 hour and 23 minutes to read Existence of Unimodular Triangulations–Positive Results by Christian Haase
Assuming a reading speed of 250 words per minute. Learn more
Description
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.
How long is Existence of Unimodular Triangulations–Positive Results?
Existence of Unimodular Triangulations–Positive Results by Christian Haase is 83 pages long, and a total of 20,999 words.
This makes it 28% the length of the average book. It also has 26% more words than the average book.
How Long Does it Take to Read Existence of Unimodular Triangulations–Positive Results Aloud?
The average oral reading speed is 183 words per minute. This means it takes 1 hour and 54 minutes to read Existence of Unimodular Triangulations–Positive Results aloud.
What Reading Level is Existence of Unimodular Triangulations–Positive Results?
Existence of Unimodular Triangulations–Positive Results is suitable for students ages 10 and up.
Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.
When deciding what to show young students always use your best judgement and consult a professional.
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