mitchkeller/applied-combinatorics

Applied Combinatorics by Mitchel T. Keller and William T. Trotter

applied-combinatorics's Issues

Typo in 6.7

Sentence near the end that reads "Erase the line joining points c and d." should read "Erase the line joining points c and j."

Typo in section 5.1

Your Name: Ethan Raymond
Your Institution: University of Toronto
Your Email: [email protected]
Subject: Chapter 5.1
Your Message: In the second paragraph of section 5.1, the second to last sentence reads in part "while a drawing of a graph is a helpful too, it is not..." I imagine this is simply a typo, and should have read tool.

Error in Corollary 8.13

Second binomial coefficient in the sum should be \binom{2n-2k}{n-k}.

Multiset counting

Consider something like Oscar's pizza topping problem in the ubiquitous nature of binomial coefficients section if we don't have sufficient things there.

Use Sage cells for some exercises

Graph algorithms could benefit from some well-chosen or random exercises where the student is given a graph and expected to carry out the algorithm, but then afterward they can evaluate a Sage cell to have the correct answer shown.

Typo in 2.2 permutations

The P(26,20) before Example 2.7 should be P(26,6).

Exercise 2, section 7.7

Please see 1 for exercise statement.

There seems to be an issue with the number of students that know Java. There are 748 such students. Since 488 know all three languages then this leaves 748-488=260 students that know Java and at most one other language. Issue arises when you compute the number of students that know only Java and C++ (639-488=151), and only Java and Python (632-488=144). Since these sets are disjoint subsets of the students that know Java, we should have 144+151\leq 260, which is not possible.

Seems like a possible fix would be to add 35 students to the Java category, or maybe a bit more so that there are students that only know Java.

Credits go to an anonymous student who reported this.

Misleading statement in Example 9.10

Csaba Biró (U of Louisville) reports an issue with a sentence in Example 9.10:

This is in Section 9.4, example 9.10. After you get the explicit formula
for this counting problem, for which the roots of p(A) are
$(3\pm\sqrt{5})/2$, you write:

"This probably looks suspicious; we're counting strings here, so t(n)
needs to be a nonnegative integer, but the form we've given includes not
just fractions but also square roots! However, if you look carefully,
you'll see that using the binomial theorem to expand the terms in our
expression for t(n) would get rid of all the square roots, so everything
is good."

This really depends on c_1 and c_2, which, at this point is not
computed. In the simple case of, say c_1=c_2=1, when you essentially
ignore the constants, only every other term cancel, and all, except for
one contain $\sqrt{5}$. Even worse, if, say, c_1=1, c_2=0.

In fact c_1 and c_2 have important roles in canceling the \sqrt{5}
terms, that's why they, themselves contain \sqrt{5}.

The point is well-taken and will be fixed. This is not being posted to the errata list at this time.

Topic dependence chart

It would be useful if the preface would give a dependency flow chart so instructors can select topics and ensure they have the pre-requisite topics included as well.

Name issue in Epilogue

From WTT:

One minor typo (no doubt there are more). In the
epilogue, in the paragraph for Yolanda, there is
an off the way reference to Zori. Change that back
to Yolanda.

conversions to be done by hand

I think these changes have to be made by directly editing the source files:

1. Use "term" not "em" for words being defined

2. Convert overpic to svg, or whatever is appropriate.

Pronoun gender

This phrase seems odd:

Dave hates doing the same thing twice. He sees herself

Typo: Section 8.1 at log(1+x)

In example 8.2, after integrating, there is a (-1)^{n+1} factor missing in \sum_{n=1}^\infty \frac{x^n}{n}.

A period seems to be missing as well (to end that sentence).

Website username example in strings chapter

There's a tabular here that really shouldn't be one, and the \end{example} is misplaced.

Example 3.3

There is a place where example 3.3 mistakenly says r(1) = 1.

Pascal's triangle tabular in induction chapter

Can we do this without a tabular? Getting converted very poorly.

Example 2.32

Should the suffix be 'RAREGENIUSES'?
Current suffix is 'RAREREGENIUSES', see 1.

Exercise 8.15.b shouldn't use e.g.f.

This doesn't work out well using exponential generating functions. Csaba Biro reported this and suggested a way to deal with it using ordinary generating functions.

LaTeX source with extra newlines in display math

introduction.tex (at least) has some equations that are of the form

[
blah
]

The MBX output has blank lines inside <me>, which then result in the LaTeX not compiling.

Typos

Here are some errors I noticed over the semester, mostly typos. Thanks again!

Chapter 2, Exercise 32 "and 0 of are painted red" should be "and 0 are painted red".

Section 5.3: missing comma in part 2 of the definition of eulerian (before "t-1")

Section 5.3: Sage code gives error "Missing parentheses in call to 'print'."

Section 5.4: Definition of proper coloring "such that if" should be "such that"

Section 5.4: Definition of bipartite graph, should be "partition of the vertex set V"

Section 5.4, right before "5.4.3 Can We Determine Chromatic Number". The line "where we show that are there graphs with large chromatic" should have "are" and "there" swapped

Section 5.6, in the Proof of Cayley's Theorem, second paragraph, "which can only happen T\cong K_2" is missing "if"

Section 13.5, in the paragraph on "First Labeled, First Scanned". In your example, you imply that vertex G is labeled twice, even though vertices can only be labeled once.

Section 16.1, second paragraph "information at to which of the" should be "as to" instead of "at to"

Section 16.4, in the definition of "stable", I (think) number 3 should be "g' prefers b to b'".

Dennis Hall, PhD
Associate Professor, Mathematics
Angelo State University

Partitions of 8 table looks really weird

The partitions of 8 table (Intro?) is coming out really weird in MBX->LaTeX.

Prüfer code tables

The Prüfer code tables are not being meaningfully converted to tables in MBX. These seem like they should legitimately be tables.

Render issue in section 7.1

Example 7.3 seems to have some issues when rendering (screenshots: 1 and 2). An inequality is displayed with double \gt signs when maybe only one is intended. Source code seems to be fine since LaTeX source does not have this problem.

Not sure if this is a MathJax issue.

Mistake in Example 8.7

Here I’d like to report a small error in Example 8.7 in Section 8.2:

In the solution, the sixth last line, as we are giving to n children, we should choose n-1 dividers, instead of k-1. Then the displayed math following the line should also be corrected.

(Jie Han from the math department, University of Rhode Island)

graphs-figs/k44-M_crop

This figure in the graphs chapter uses the picture environment to do something that you'd normally accomplish with overpic. Probably best to go re-code this.

Missing "theorem" 7.14

On this page
http://rellek.net/book/s_inclusion-exclusion_euler-phi.html
It says "Our proof of 7.14", which is missing the word "Theorem".

In the proof if Proposition 7.15, similar error, but the word "Proposition"
is missing.

Opening the 7.14 knowl in "Our proof of 7.14", the equation appears as LaTeX,
not rendered by MathJax. (Seems to be due to a label and tag in the equation,
which probably comes from a PTX error, which may already have its own issue.)

Location of linear order definition

Was looking at example 6.7 4, see 1, and it seems that the term "linear order" is used before it is defined. Definition appears 3 paragraphs later in that section, see 2. Is this an issue?