# Combinatorial Mathematics - Fall 2005 Typos

## Category 1: Mathematical typos/corrections to text

• p12, complexity: the statement about f\in O(g) defining an equivalence relation is nonsense and has been eliminated (Noah Prince)
• p23, before Proposition 1.1.17: the emptyset sign should just be blank space
• p36, Exercise 1.2.13(d): the upper limit of the sum on the right should be n, not n+1
• p52, Exercise 1.3.13: "nn,k" should be "an,k"
• p72, Exercise 2.1.41: "{2\choose n}n" should be "{2n\choose n}"
• p110, Example 3.1.9: "even number of times, the factor for it is x2+x4+..." should be "even number of times, the factor for it is 1+x2+x4+..." (Jung-Jin Lee)
• p119, Exercise 3.1.21c: the limits on the index of summation should be specified as 0 and n to avoid confusion with the extended binomial coefficient when k > n (Milos Curcic)
• p119-20, Exercises 3.1.21,23: "OGF" should be "generating function"
• p130, Example 3.2.18: "(1-x)-(k-1)" should be "(1-x)-(k+1)" (Jung-Jin Lee)
• p134, Exercise 3.2.15: the index of summation on the left should be n, not k
• p135, Exercise 3.2.19: "m-2k)" should be "m-2k"
• p163, Remark 3.4.6: the sign of the exponent on "\sqrt{n}/e" is wrong (Jung-Jin Lee)
• p164, Theorem 3.4.7: in the first expression for lnP(x), the coefficient 1 should be -1. Later, "t/(1-t)" should be "x/(1-x)"
• p271, Proposition 5.2.3: in the proof, "$ki/l$" should be "$ki$" (Deepak Ramachandran)
• p363, Lemma 7.2.16: "Deleting y from these paths" should be "Stopping these paths where they reach U (Jung-Jin Lee). The converse should be proved by showing that if G is not k-connected, then there is a pair (x,U) such that there is no x,U-fan.
• p382, Theorem 7.3.10: the hypothesis that n \ge 3 should be added
• p433, Exercise 8.3.34: in the condition, the parity edge-coloring should have k colors
• p519, Exercise 10.1.15: "order of a divides p" should be "order of a divides p-1"
• p905, Example 17.1.22: in the matrix, position (3,4) should be "-b2", not "b2" (Vicki Reuter)
• p927, Lemma 17.2.33: "O(x)" should be "R(x)"

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

• p127, before Example 3.2.12: "3.2.6(4)" should be "3.2.6(2)"
• p685, Theorem 13.2.19: "??" should be "Exercise 12.1.11"
• p897, Lemma 17.1.3: "every position below the first row" would be clearer as "a particular position below the first row"

## Category 3: Minor typos and corrections

Note: Corrections involving addition, deletion, or alteration of one punctuation mark may be implemented without being listed here. Some corrections to capitalization are also omitted.
• p26, Exercise 1.1.9: "orders" should be "orderings"
• p52, Exercise 1.3.14: "eR(Rey" should be "(Rey"
• p54, Exercise 1.3.24: "candidate b" should be "candidate B"
• p62, bottom line: "arise" should be "arises"
• p84, Remark 2.2.17: "finsih" should be "finish"
• p169, before Lemma 3.4.16: the arrows in the middle figure are hard to read; they should point up
• p183, Theorem 4.1.8: "2004, p>" should be "2004, p." Later, "not distinguish" should be "not distinguishable"
• p311, Example 6.1.7: "each composes" should be "each composed"
• p321, bottom: "differ from" should be "different from"
• p484 bottom: "their unavoidable of" should be "their unavoidable set of"
• p625, Exercise 12.2.16: "two smaller one" should be "two smaller ones"
• p636, Exercise 12.3.10: "argue that that" should be "argue that"

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