# Combinatorial Mathematics - Fall 2006 Typos

This page lists the typographical errors that have been discovered in the Fall 2006 pre-publication version of Combinatorial Mathematics, by Douglas B. West. This page is of interest only to those persons having a copy of this draft, particularly the students in my course, other users of the text, and reviewers. Please send comments and corrections on the book to west @ math.uiuc.edu. Contributors are noted in parentheses. Please do not send comments about incorrect page numbers in the index (and note that all page numbers there are odd for \TeX nical reasons); however, I do want to know of missing terms that should be added to the index.

## Category 1: Mathematical typos/corrections to text

• p38, Exercise 1.2.17: Change the upper limit on the right side to m. The statement is correct either way, but the change makes the problem cleaner. Also delete the condition that m < n+r; it is unnecessary.
• p91, Theorem 9.3.11: Add parenthesis in first displayed equation (Kyle Jao)
• p112, Example 3.1.9: In the discussion of even usage, the term "1" was missing from the factor for such a type.
• p134, Example 3.2.20: At the end, "(-1)n-m/2" should be written as "(-1)n+m/2", even though they have the same value. (Chun-Cheng Chen)
• p158, Exercise 3.3.6: drop the factor (-1)k (Chun-Cheng Chen)
• p184, bottom: The sentence starting with Theorem 4.1.4 is a vestige of an old version. However, if you think about the proof of Theorem 4.1.4, this is actually what it does.
• p210, Exercise 4.1.59: The set T does not include (0,0) or (r,s). This can be accomplished by putting strict inequalities in the restrictions on T, though it is not necessary to be quite that restrictive. (Tracy Grauman)
• p264, Proposition 5.1.20: "remaining three vertices" should be "remaining three elements"
• p274, Proposition 5.2.5: "four integer corners" should be "zero or two or four integers corners"
• p351, Theorem 7.1.8: The wrong symbol was used for the cartesian product of the two vertex sets; it should be \Box for the graphs and \times for the vertex sets.
• p354, Theorem 7.1.15: "S'" should be "\bar{S}" throughout, since we are discussing an edge cut. (Vinicius Lopes)
• p412, Lemma 8.2.9: "V(G-v)" should be "V(G-x)"
• p423, Exercise 8.2.32: "not r-colorable" should be "r-colorable", and "L'(y)" should be "|L'(y)|"
• p491, Corollary 9.3.12: "\chi'l(G)=\chil(G)" should be "\chi'l(G)=\chil(L(G))" (Kyle Jao)
• p915, Theorem 17.1.23: The hypothesis should require that this is a symmetric design.
• p955, Exercise 17.3.1: "STS(9)" should be "STS(v)"

## Category 2: Comments, clarifications, and cross-references

• p20, Example 1.1.9: "so equality holds" is the end of the proof of the first statement (equality of size). Thus "If some element" should start a new paragraph for the proof of the second statement (the functions are bijections).
• p37, Exercise 1.2.31: The problem is being changed to give the value of the sum: (n+1)/(n-m+1). Now prove it!
• p199, after Example 4.1.34: "Exercise 60" should be "Exercise 59" (the requested cross-referencing was correct, but a hidden exercise was counted by a perl script to produce the misnumbering) (Tracy Grauman)
• p405, Remark 8.1.16: "Exercise 18" refers to Exercise 8.2.18, not Exercise 8.1.18. The exercise is moving to replace Example 8.1.15.

## Category 3: Minor typos and corrections

Note: Corrections involving addition, deletion, or alteration of one punctuation mark may be implemented without being listed here. Corrections to capitalization may also be omitted.
• p29, Exercise 1.1.37: "by count" should be "by counting"
• p56, Exercise 1.3.29: "set triangulations" should be "set of triangulations"
• p70, Exercise 2.1.12: "each each" should be "each" (Kyle Jao)
• p179, Exercise 3.4.31: There is an extra "is k(k-1)".
• p170, Theorem 3.4.13: "Thes parts" should be "These parts" (Tracy Grauman)
• p465, Exercise 9.1.19: delete "05F"
• p490, Theorem 9.3.11: delete one "G" (Kyle Jao)
• p491, Theorem 9.3.11: in the first display, a right parenthesis is missing

Archive of corrections to earlier versions: Fall 2005, Fall 2004, Fall 2003, Fall 2002.