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

SIXTH EDITION
p. xii, line 6 after display: ". . position 2 in Guess 4 would earn . ."
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. 29, Exer 8. Hint should read: How many edges in Kn?
p. 67, Exer 8c, should 4(o).
p. 139, 2nd line before Example 2, the Greek letter phi should be 'f'.
p. 141, Example 3, end of 3rd para. "hence", not "whence"
p. 143, End of Example 3 (continued) should be Figure 4.7g.
p. 156, last para.:"Next we show that if |R(A)|>=|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 PhaseI, should be "x21 = min(60,20)=20".
p. 183, line after e c e (underlined) should start: It was generated in two cases . .
p. 199, Exer. 10, the letter 'd' is missing from the list of letters.
p. 202. Ex. 48, replace "decimal" by "ternary"
p. 207, line 3., "(see Exercise 37)"
p. 237, Answer to Sect. 5.1, Exer. 13c. Should start "If leftmost digit is 3, there are no constraints - 9^5."
p. 238 Exer 49 Answer, part (a), last term in answer should be 4!
p.268 Example 2, line 2 'partions' should be 'partitions'
p. 270, Exer. 20, replace 2 by 1/2 in expression.
p.275, Ex. 1, end of line 1, 'arrangements of r'
p. 277, line 5-6 of Sect 6.5 'xn' should be x^n'
p. 290, line 2, "an = an-1 + 3^(n-1)"
p. 300, line -5, lower bound for i should 1, not 0
p. 315, Exer 3b, after equation should read "(n > 3), a sub 2 = a sub 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. 336, formula for N2, should start"S2 - C(4,3)S3 = .."
p. 340, Exer. 46a, replace r by k in formula and constraint on r.
p. 370. line -7, end of line replace 'pi' by 'x'
p. 394, breakout near bottom of page, second line should end "s(x2)]".
p. 397, Figure 10.8 is flawed: first line should be 2 = 0 1 0 , and digital sum should be 1 1 0 = 6,and
p. 297 Example 9, The digital sum in line 2 should be 2+2+3+4 = 6,
and the second para. should be:"Since the sum row has 1's in the 2^2, 2^1 and 2^0 columns, we must change the 1 in the 2^2 to 0 and the 0's in the 2^2 and 2^0 columns to 1. That is, pile's 4's binary expansion should be changed from from 100 to 011, and so player A should remove 1 stick in the 4th pile. This new positionn (2,2,3,3) has a Grundy number of 0." [Then continue with same last sentence.]
p. 403, Table P.1, the number over B should be 5.
p. 412, Exer. 2 "Decode this cryptogram (note the sequence JPLENFYV occurs .."
p. 442, Section 1.1 Ex. 15 (a) 5 other pairs. (b) {b,j},{c,h} and 7 other pairs.
p.443, Section 1.3: EXec 1. (a) 8, (b) 13, (c) 8 or 12 or 16 or 24 or 48.
Sect 1.3: Asnwers for #5,7,9,13 should be for #7,9,11,15, respectively
p. 457, Sect 5.1 Exer 17a), second part 10x9x8^(n-1)
Sect 5.1, Exer.37: Break into case for 3 different values for smallest and largest: if 1 and 2, then each die can be 1 or 2-- 2^3 choices-- minus the case where all are 1 or all are 2, and so answer in this case is 2^3 -2; if 2 and 4, then each die can be 2 or 3 or 4-- 3^3 choices-- minus the cases where all are 2 or 3 and all are 3 or 4-- 2x2^3 possibilities, and so answer in this case is 3^3 - 2x2^3. Reader can do case of 3 and 6.
(still p.457) Sect 5.2 Exer. 15 replace 9 by 8.
p. 458, Exer. 27 , 2nd part, 6x(5!)^2/10! (6 is no. of possible patterns of v’s and c’s)
Exer. 51, divide answer by 4!.
Exer. 71c third term should be [C(23,2)xC(23,1)]
Exer. 79 multiply last term in parentheses by 2
p.459, Sect 5.4:3a) C(13,4)C(13,4)C(13,2)C(13,3)/C(52,13).
p. 462, Sect 6.2: Exer 1111e) b^(11)xC(11,m)
p. 463, Sect 6.5: Exer 5b) minum sign in front
p.465, Section 7.3, Exer. 1a, (1.08)^n*500.
Sect 7.4: Exer 5 an = an-1 + 1 + existing summation
Exer 7 replace 1250 by 2500
Exer 17 replace b2^n by B3^n
Sect 7.5: Exer 1b replace -3 by -3x
p. 467, Section 8.2: NUMBERING IS OFF for 35, 37, 39, 41; they are answers for problems 37, 39, 41, 49 respectively, and the answer for 35 is: C(8x7x6,8) - C(8,1)C(7x6x5,8) + C(8,2)C(6x5x4,8) - C(8,3)C(5x4x3,8) + C(8,4)C(4x3x2,8).

FIFTH EDITION
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.397, Example 1, line 2: first number in digital sum should be 2, not 1. Same correctioN for first number in Figure 10.8, so that sum should be 1 1 1 = 7.
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. 440, Sect 1.4, Ex 11(a) should read "..R1 and R2 - 2x(no. of common edges."
p. 444, Exer. 11a: Curcuit length = sum of number of boundary edges of R1 and R2 - 2x(no. of edges interior to circuit).
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.