### Corrections to Applied Combinatorics, 6th and 5th edition.

SIXTH EDITION
p.18, Figure 1.11, right graph, at 7, edge should go out to 6 and come in from 8.
p. 29, Exer 7, . . . . has $$(1 + \sqrt{8m+1} )/2$$ vertices.
p. 66, Exer 8c, should 4(o).
p. 156, last para.:"Next we show that if $$|R(A)|\ge|A|$$ ... "
p. 161, Exer 8, last line: 'Bears' should be 'Vikings'.
p. 166, Fig 4.18: edge (3,2) should be darkened, edge (3,1) should not.
p. 168. 2nd para. of Phas I, should be "x21 = min(60,20)=20".
p. 183, line after e c e (underlined) should start: It was generated in two cases . .
p. 207, line 3., "(see Exercise 37)"
p. 238 Exer 49 Answer, part (a), last term in answer should be 4!
p. 270, Exer. 20, replace 2 by 1/2 in expression.
p. 290, line 2, "$$a_n = a_{n-1} + 3^{n-1}$$"
p. 315, Exer 3b, after equation should read "($$n > 3$$), $$a_2 = a_3 = 1$$ "
p. 323, second line "developed in Chapter 5."
p. 324, In breakout expression after 4th line, there should be bars over the A's on the right side of the equation.
p. 334, Line after breakout near top, "See Exercise 38 . ."
p. 340, Exer. 46a, right-side should be $$C(n-m,n-k)$$
p. 394, in breakout equation near bottom of page, the end of the second line should read "s(x2)}"
p. 412, Exer. 2: in note, the correct repeated sequence is JPLENFYV.
p. 443, Sect. 1.3, Exer. 1 (a) 8, (b) 13, (c) 8, 12, 16, 24 or 48
p. 457, Sect 5.1, Ex 37: answer should be "$$36/3^6$$-- count ways to realize the 9 possible unordered triples of dice values, i.e., 6,6,3; 6,5,3; . . . .; 2,1,1,
p. 458, Sect 5.2, Exer. 51, given answer should be divided by 4!.
p. 459, Sect. 5.4, Exer. 3a $$C(13,4)^2*C(13,2)C(13,3)/C(52,13)$$
p.467, Sect. 8.2, Exer 35,37,39, 47 should be numbered 37,39,41,49
Section 8.2, 35. $$C(P(8,3),8)-8C(P(7,3),8)+C(8,2)C(P(6,3),8)- C(8,3)C(P(5,3),8)+C(8,4)C(P(4,3),8)$$
FIFTH EDITION
p. xi, in Mastermind scoring table heading, to the left of "Secret Code" should be the sequence R Bu Y Y; "Scoreing" should not have an 'e'.
p. 28, Exer. 5, . . .has [1 + sqrt(1 + 8m)]/2 vectices.
p. 41, Exer 20, at end of problem, should read "at LEAST k".
Exer 21, should be Exercise 3(l).
p. 94, Theorem 1 (a) should read "T has no circuits."
p. 111, Exer. 16(b), "an objective of 2 quarts in one pitcher".
p. 119, last line, should be S1 = C*-e*.
p. 124, Exer 3, should refer to Exer 17, not 13, in Sect 3.1.
p.154, Figure 4,13. The second label of node a should be 'infinity'
p. 164-171, in all the Figures and graphs, the cost of c22 should be 6 and c31 should be 7.
As a consequence of this change, all calculations that involve c22 have to be changed. The following 5 pages of corrections follow:
p.165, l. 3, change $7 to$6 and the sum from $630 to$600
p.166, l.6, change 7 to 6; l.6, "= 10"; l. 8, net change is 10-12 = -2; l.9, "the solution by 2."
last sentence in 2nd para., "has a cost of $580 which, as expected, is$20.."
p.169, l.11, v2 = $8 +$6= $14; display (1): v2 =$14, u3 = v3 = $8. p.170, in breakout after l. 2, replace$15 by $14 and$9 by $8 (two places), second line should be =$1700 - $1120 =$580 In Step II.B: end of l.2, change $15 to$14; beginning l. 5, change $3 to$2; in display (4): edge (1,2) "=$14-$10=$4 decrease of$2";
edge (1,3) "=$8-$10= -$2 increase by 2; edge (2,3) "c23 =$0 = v3 - u2 = $8 -$8 = $0 no change"; edge (3,1) "c31 =$7 > v1 - u3 = $14 -$8 = $6 increase of$1"
later on p.170: beginning of line -7 "2+6-4-6=-2"; l.-6 "will ave $2"; beginning of l.-3 "shipments in (2,1) and (1,2)"; l.-2 "40x$2 = $80" p. 171, display (5): v1 =$12, u2 = $6; display (6) edge (1,1):"c11=$4 > v1-u1=$12-$10=$2 increase of$2";
edge (1,3):"c13= $0 > v3-u1=$6-$10=-$4 increase of $4"; edge (2,3):"c23=$0 = v3-u2=$6-$6=$0 no change"; edge (3,1): "c31=$7 > v1-u3 = $12-$6=$6 increase of$1."
Also on p. 168, Figure 4.21: Supply for Warehouse 2 (on the right) should be 40, not 20.
p. 173, Exer 6, the second mention of store 2 should be 'store 3'
line 7, should be "x13 = min (40,20) = 20. . ."
p. 185, Exer 26, should be"an integer from 0 to 9,999.."
p. 231, Ex. 27a. in sum, 'denominator' in bin. coeff. should be j, then j+1, going p to k, where 1
p. 235, Exer 45 Answer part (a)-- last term in answer should be 4!
p.257, in first breakout, the expansion of g(x) should have all positive terms.
p. 396, Fig 11.2: no edges should go out from vertices 4, 9, 16, or 36.
p. 424, at the end of Example 2, the parenthetical remark should be "See Exer. 15"
p. 439, Sect 1.3, Ex. 5, 'z' should be '2'L 1.4: Ex 3d, delete e.
Sect 1.4 3d, should read 'delete e'.
p. 449, Sect 3.4, Ex. 3 should refer to Exer 17, not 13, in Sect 3.1.
p. 453, Sect 5.1, Ex. 17a (at end of answer) Exponent of 8 should be n-1.
Ex 23b,should be 8^3*7 + 1
p. 455, Sect 5.4, 3b, denominator should be '(52!/13!^4).
Sect 5.4, 9a C(9,4) instead of C(19,4).
p. 458, Sect 6.2, Ex. 29 remove the '}' in the second line.
p. 462, Sect 8.1, Ex. 7 the plus sign should be a minus sign.
p. 463, Sect 8.2, Ex. 11 last term should be C(3+6-1,3)
p. 465, Sect 9.3, Ex. 7.e 2nd term should be 2m^2.