``Order and Optimization (TAC: Vol. III)'' - Typos
This page lists the typographical errors that have been discovered in
the Fall 2006 pre-publication version of
Order and Optimization, by Douglas B. West (Volume III of
The Art of Combinatorics).
This page is of interest only to the few persons having a copy of this
draft, such as the students in my course and possibly reviewers.
Please send any additional contributions to west@math.uiuc.edu.
Contributors noted in parentheses.
Category 1: Corrections of a Mathematical Nature
- p9, Example 0.24: "a0" should be
"a1" (Alexandra Seceleanu)
- p32, Exercise 11.1.5: "Ci\times Cj" should be
"\underlin{i}\times \underlin{j}" (Tim LeSaulnier)
- p41, Example 11.2.20: "the k-shadow of A lies in"
should be "the set A* of elements covering elements of
A is precisely"
- p52, Example 11.3.4: "element of BNn" should be
"member of 2n:
- p62, Theorem 11.3.18: The chain labeled D0 in the
figure should be labeled D1. In the text,
"a3=3" should be "a3=n-1"
- p174, Exercise 12.3.3: "2k-dimensional posets" should be
"posets of dimension at most 2k".
- p188, Exercise 12.4.2b: in the hint, "at most" should be "at least"
(Paul Wenger)
- p221, top: in the case of one vector having 10 and the other having
01, the intersection remains unchanged if the second vector doesn't change,
so this case should also allow equality.
- p231, Theorem 13.1.31: In the middle paragraph, we must prove that
B\esub T in order to put B into H. This uses the
maximality of T. The final paragraph does not need the
maximality of T.
- p258, Theorem 13.3.3: several instances of "I(x)" and "C(x)"
should be "I(x1)" and "C(x1)"
- p259, Theorem 13.3.3: At the end of the proof, the claim that
xi < I(xi-1) does not follow, but the choice of
xi does imply that every element strictly below
xi (such as all of I(xi+1)) is below
all of I(xi-1), and this is enough
- p262, Example 13.3.9: "intervals of size n" should be
"intervals of size i"
- p479, Theorem 15.3.36: in the last paragraph,
C' should be Y
Category 2: Other Changes, Comments and Corrections of Note
- p219, Theorem 13.1.8: the term "shade" was used before its definition
- p223-225, Kruskal-Katona: Uses of "reverse lexicographic" should be
changed to "colex", since some readers might misinterpret "reverse
lexicographic" to mean the reverse of lexicographic order" (Garth Isaak)
Category 3: Minor Changes, Typos, and Clarifications
- p40, Theorem 11.2.17: "be real-valued weight" should be "be a real-valued
weight"
- p135, Remark 12.2.9: "not surprised" should be "not surprising"
- p228, Theorem 13.1.27: "It suffice" should be "It suffices
- p259, top: "monchromatic" should be "monochromatic", and three lines
later a parenthesis is missing
- p394, Definition 15.1.4: the last "that" should be deleted