# Order and Optimization (TAC: Vol. III)'' - Typos

This page lists the typographical errors that have been discovered in the Fall 2004 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 Exm0.24: in the notation for an element of L(m,n), "a0" should be "a1" (Gexin Yu)
• p22 Lem11.1.17: the definition of canonical decomposition was omitted
• many pages: the change to bold k for k-element chain has not yet propagated throughout the book
• p66 Prop 11.3.24: "N(S)\ge|S|" should be "N(S)\ge|S|"
• p72 Exr11.3.3: "t=n" should be "xt=n"
• p86 Lem11.4.27: the statement should be that P(L) and Q(L) are isomorphic, not asymptotic. The proof depends on the fact that the dual of a distributive lattice is also distributive and should mention this.
• p89 Exr11.4.7: part (b) is nonsense; delete it (it refers to the dominance order in the next exercise)
• p132 Exm12.2.11: "d < e" should be "d < e < f"
• p156 Def12.3.1: the requirement for a normal bipartite poset should be that the comparability graph is connected and that for each choice of x and y from the same level, there is an element comparable to x but not to y (Kevin Milans)
• p158 Lem12.3.7: the statement should be restricted to normal bipartite posets (Kevin Milans)
• p232 Thm13.1.32: the two instances of "F" should be "F"
• p314 before Exm14.1.34: "c/2 log n" should be "(c/2)log n"
• p335 Thm14.2.19: the necessary condition that p and q have the same sum needs to be added (Reza Zamani)
• p340 Thm14.2.24: the two instances of "flow" in the statement should be "feasible flow"
• p403 Cor15.2.15: "r(e)" should be "r(E)" (Garth Isaak)
• p408 Exr15.1.21: "transversal matroid" should be "partition matroid"
• p409 Exr15.1.28: Part (b) is false; there is a counterexample within the cycle matroid of K4 (Ashutosh Mahajan)
• p454 Before Prop15.3.5: strike "connected" twice; the dual of every matroid is a matroid with the same components. The proposition repeats Exr15.1.42, which will be removed.
• p472 Lem15.3.38: "obtain a in which" should be "obtain a minor in which
• p487 Def15.4.19: "every set" should be "every nonempty set" (Kevin Milans)
• p488 Thm15.4.22: "Applying C" should be "Applying B". The arguments here are all local and do not require E\inF. Hence the equivalence holds more generally for shellable systems, which is used in Theorem 15.4.61. This means that the definition of shellable system should be moved earlier, and Theorem 15.4.22 should be stated for that context. (Kevin Milans)
• p520 Exr15.4.20: "nontrivial greedoid" should be "full greedoid", and "x,y" should be "e,f"

## Category 2: Other Changes, Comments and Corrections of Note

• p39 Rem11.2.14(4): "Chapter 6" should be "Section 11.3"
• p45 Thm11.2.25: the proof is being rephrased in probabilistic language
• p45 Thm11.2.26: parentheses are being added on "k+1" is the statement. In the proof, it should be noted that "Ai\cup Bi omits k elements" depends on the observation that we may assume that the chains in a copy of the subposet with the most chains do not skip levels.
• p53 Exm11.3.6: The reference to "11.3.6" should be to "11.3.4"
• p54 Exm11.3.9: The reference to "11.3.6" should be to "11.3.4"
• p85 Thm11.4.25: the proof does not need to check that ideal map is both a poset isomorphism and preserves meets and joins; each of these implies the other (Erin Wolf)
• p230 after Conj13.1.30: "Kleitman [1981]" should be "Kleitman [1979]" (Bruce Sagan)

## Category 3: Minor Changes, Typos, and Clarifications

• p19 Def11.1.9: "Then" should be "The"
• p88 Thm11.4.31: "a arbitrary x,y,z with z\le x in a lattice" should be "any x,y,z\in L with z\le x"
• p94 Exr11.4.24: This exercise should be combined with Exr11.4.7
• p169 before Thm12.3.27: "a arbitrary" should be "an arbitrary"
• p462 Exm15.3.23: the family B was never actually defined (and an "of" is missing