invindex.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

246: binomial coefficients\sub reciprocal of
246: convolution
246: double sums
246: indefinite summation\sub of binomial coefficients
246: partial fraction expansions\sub powers of
247--248: Gosper\sub algorithm, examples
247: Gau{\ss} (= Gauss)\sub identity for hypergeometrics
247: Pfaff\sub reflection law
247: degenerate hypergeometric series
247: hypergeometric series\sub degenerate
247: hypergeometric series\sub transformations of
247: reflection law for hypergeometrics
247: unexpected sum
248: Vandermonde's convolution\sub generalized
248: asymptotics\sub of binomial coefficients
248: binomial coefficients\sub asymptotics of
248: indefinite summation\sub of binomial coefficients
248: summation\sub factors
249: Harry, Matthew Arnold, double sum
249: double sums
249: minimum
250: Pascal's triangle\sub variant of
250: nu function: sum of digits\sub binary (radix $2$)
250: repertoire method
250: sideways addition
250: subfactorial
250~(exercise~75): binomial coefficients\sub wraparound
251: Pascal's triangle\sub hexagon property
251: Pascal's triangle\sub row lcms
251: asymptotics\sub of binomial coefficients
251: binomial coefficients\sub asymptotics of
251: hexagon property
251: least common multiple\sub of $\{1,\ldots,n\}$
252: binomial series
252: generalized binomial series
252: multinomial coefficients\sub recurrence for
253--254: Gosper\sub algorithm, examples
253: Clausen\sub product identities
253: Whipple\sub identity
253: hypergeometric series\sub transformations of
254--255: Gosper-Zeilberger algorithm\sub examples
254--255: algorithms\sub Gosper-Zeilberger
254: binomial coefficients\sub reciprocal of
254: useless identity
255--256: binomial coefficients\sub middle
255--256: proper terms
255: Ap\'ery\sub numbers
255: double sums\sub telescoping
255: telescoping
255: trinomial coefficients
256: rewards
257--267: Stirling numbers
257--319: special numbers
257: Karamata, Jovan
257: Stirling
258--259: counting\sub set partitions
258--259: partitions\sub of a set
258--262: Stirling numbers\sub combinatorial interpretations
258: Stirling
258: Stirling numbers\sub of the second kind
258: Stirling numbers\sub table of
258: Stirling\sub triangles
258: empty case\sub for Stirling numbers
258: null case\sub for Stirling numbers
259--262: counting\sub cycle arrangements
259--262: cycles\sub of permutations
259--262: permutations\sub cycles in
259: Stirling numbers\sub of the first kind
259: Stirling numbers\sub table of
259: Stirling\sub triangles
259: addition formula for ${n\choose k}_{\mathstrut}$\sub analogs for $n\brace k$ and $\,n\,\brack k$
259: necklaces
260: Kipling, Joseph Rudyard
260: bicycles
260: triangular numbers
261: absorption identities
261: addition formula for ${n\choose k}_{\mathstrut}$\sub analogs for $n\brace k$ and $\,n\,\brack k$
262--263: falling factorial powers\sub related to ordinary powers
262--263: graphs of functions\sub $1/x$
262: counting\sub permutations by cycles
263: rising factorial powers\sub related to ordinary powers
264--265: Stirling numbers\sub identities for
264: inversion formulas\sub for Stirling numbers
266: notation\sub extension of
267--268: Eulerian numbers\sub combinatorial interpretations
267--268: ascents
267--268: counting\sub permutations by ascents
267--268: permutations\sub ascents in
267--271: Eulerian numbers
267: Euler
267: Knuth
267: Stirling numbers\sub duality of
267: Stirling numbers\sub table of
267: Stirling\sub triangles
267: duality\sub between Stirling numbers of different kinds
267: notation\sub need for new
268: Euler\sub triangle
268: Eulerian numbers\sub table of
268: addition formula for ${n\choose k}_{\mathstrut}$\sub analog for ${n\euler k}_{\mathstrut}$
268: computer algebra
268: symmetry identities\sub for Eulerian numbers
269: L\u{\i} Sh\`anl\'an R\'ensh\=u [= Qi\=ur\`en]
269: Stirling numbers\sub identities for
269: Worpitzky\sub identity
269: squares
269: sums\sub of consecutive squares
270--271: Eulerian numbers\sub second-order
270--271: second-order Eulerian numbers
270: Gessel, Ira Martin
270: Stanley, Richard Peter
270: ascents
270: multisets
270: permutations\sub ascents in
270: product of consecutive odd numbers
271--272: Stirling numbers\sub generalized
271--272: Stirling\sub polynomials
271--272: generalized Stirling numbers
271--272: polynomials\sub Stirling
271: notation\sub extension of
272--282: harmonic numbers
272: Stirling numbers\sub convolution formulas
272: Stirling numbers\sub identities for
272: convolution\sub Stirling
272: convolution\sub identities for
273--274: cards\sub stacking
273--274: center of gravity
273--274: gravity, center of
273--274: stacking cards
273: Sharp, Robert Thomas
273: harmonic numbers\sub table of
274--275: rubber band
274--275: worm\sub on rubber band
274: Kafkaesque scenario
275--276: harmonic series
275: summation\sub factors
276--277: approximation\sub of sums by integrals
276--277: sums\sub approximation of
276--278: asymptotics\sub of harmonic numbers
276--278: harmonic numbers\sub asymptotics of
276: ln: natural logarithm
276: logarithms\sub natural
276: natural logarithm
277--278: Riemann's zeta function\sub as generalized harmonic number
277--278: zeta function\sub as generalized harmonic number
277: Euler
277: Newton
277: generalized harmonic numbers
277: harmonic numbers\sub generalized
277: harmonic numbers\sub second-order
277: second-order harmonic numbers
278: Brahma
278: Euler
278: Euler\sub constant ($\approx0.57722$)
278: Tower of Brahma
278: rubber band
278: stacking cards
278: worm\sub on rubber band
279--282: harmonic numbers\sub sums using summation by parts
279--282: sums\sub of harmonic numbers
279: summation\sub by parts
280--281: difference operator\sub $n$th difference
280: cards\sub stacking
280: harmonic numbers\sub second-order
280: second-order harmonic numbers
283--285: sums\sub of consecutive $m$th powers
283--290: Bernoulli numbers
283: Bernoulli, Jakob (= Jacobi = Jacques = James)
283: cubes
283: generalized harmonic numbers
283: harmonic numbers\sub generalized
283: sums\sub of consecutive cubes
284--285: perturbation method
284: Bernoulli numbers\sub table of
284: implicit recurrences
284: recurrences\sub implicit
284: squares
284: sums\sub of consecutive squares
285--286: hyperbolic functions
285--286: phi ($\approx1.61803$)\sub in solutions to recurrences
285: Bernoulli numbers\sub generating function for
285: generating functions\sub for Bernoulli numbers
286--287: trigonometric functions\sub related to Bernoulli numbers
286: Bernoulli numbers\sub asymptotics of
286: Euler
286: Riemann's zeta function\sub as generalized harmonic number
286: Riemann's zeta function\sub evaluated at integers
286: asymptotics\sub of Bernoulli numbers
286: cotangent function
286: generalized harmonic numbers
286: harmonic numbers\sub generalized
286: pi ($\approx3.14159$
286: zeta function\sub as generalized harmonic number
286: zeta function\sub evaluated at integers
287: Bernoulli numbers\sub relation to tangent numbers
287: Logan, Benjamin Franklin (= Tex), Jr.
287: Taylor
287: tangent function
287: tangent numbers
288--290: sums\sub of consecutive $m$th powers
288: Bernoulli numbers\sub calculation of
288: Faulhaber, Johann
288: squares
288: sums\sub of consecutive squares
289--290: Stirling numbers\sub related to Bernoulli numbers
289: cubes
289: sums\sub of consecutive cubes
290--301: Fibonacci numbers
290: Fibonacci numbers\sub table of
290: Stirling numbers\sub convolution formulas
290: Stirling numbers\sub identities for
290: Stirling\sub polynomials
290: convolution\sub Stirling
290: polynomials\sub Stirling
291--292: Fibonacci numbers\sub combinatorial interpretations of
291--292: reflected light rays
291: Fibonacci numbers\sub and sunflowers
291: ancestor
291: bee trees
291: drones
291: phyllotaxis
291: sunflower
291: trees\sub of bees
292--293: Cassini\sub identity
292: Cassini, Jean Dominique
292: Fibonacci
292: Lucas
292: Mersenne\sub numbers
292: optical illusions
293: Carroll
293: Fibonacci numbers\sub table of
293: magic tricks
293: optical illusions
293: paradoxes\sub chessboard
294: Mati{\t\i}asevich (= Matijasevich), \t{I}uri{\u\i} (= Yuri) Vladimirovich
295--296: Zeckendorf\sub theorem
295: algorithms\sub greedy
295: greedy algorithm
296--297: Fibonacci\sub addition
296--297: Fibonacci\sub number system
296--297: number system\sub Fibonacci
297--300: Fibonacci numbers\sub ordinary generating functions for
297--300: generating functions
297--300: generating functions\sub for Fibonacci numbers
297: Moivre, Abraham de
297: Stirling
297: carries\sub in Fibonacci number system
297: de Moivre, Abraham
298--299: partial fraction expansions
299--300: Fibonacci numbers\sub closed forms for
299--301: $\phi$ ($\approx1.61803$): golden ratio
299--301: phi ($\approx1.61803$)
299: Binet, Jacques Philippe Marie
299: Euler
299: Navel research
299: Phidias
299: golden ratio
300: Cassini\sub identity
300: nearest integer\sub rounding to
300: rounding to nearest integer
301--303: Euler
301--309: continuants
301--309: polynomials\sub continuant
301: Fibonacci\sub number system
301: continued fractions
301: fractions\sub continued
301: kilometers
301: miles
301: number system\sub Fibonacci
302--303: Morse, Samuel Finley Breese, code
302: Fibonacci numbers\sub and continuants
302: Fibonacci numbers\sub combinatorial interpretations of
303--304: Euclid\sub algorithm
303--304: algorithms\sub Euclid's
303: Binet
303: Cassini\sub identity, generalized
303: Euler\sub identity for continuants
303: continuants\sub Euler's identity for
303: symmetry identities\sub for continuants
304--309: continued fractions
304--309: fractions\sub continued
304: Lagny, Thomas Fantet de
304: de Lagny, Thomas Fantet
305--306: Stern--Brocot tree\sub related to continued fractions
305: Halphen, Georges Henri
306--307: Euler\sub constant ($\approx0.57722$)
306: Brent, Richard Peirce
306: Stern--Brocot number system\sub related to continued fractions
306: Stern--Brocot number system\sub representation of $\gamma$
306: irrational numbers\sub continued fraction representations
306: partial quotients
307--308: Fibonacci\sub odd and even
307: Davison, John Leslie
307: Einstein
307: Fibonacci\sub number system
307: God
307: generating functions\sub for spectra
307: number system\sub Fibonacci
307: spectra\sub generating functions for
309: cards\sub stacking
309: center of gravity
309: gravity
309: stacking cards
310: $\phi$ ($\approx1.61803$): golden ratio
310: $\vartheta$
310: Cassini\sub identity
310: Eulerian numbers
310: Fibonacci\sub number system
310: Stirling numbers\sub inversion formulas for
310: derivative operator\sub converting between $D$ and $\vartheta$
310: inversion formulas\sub for Stirling numbers
310: kilometers
310: miles
310: number system\sub Fibonacci
310: operators\sub derivative ($D$)
310: operators\sub equations of
310: operators\sub theta ($\vartheta$)
310: phi ($\approx1.61803$)\sub continued fraction for
310: rabbits
310: theta operator\sub converting between $D$ and $\vartheta$
311: Stirling numbers\sub generalized
311: Stirling numbers\sub identities for
311: Stirling\sub polynomials
311: generalized Stirling numbers
311: harmonic numbers\sub complex
311: harmonic numbers\sub divisibility of
311: harmonic numbers\sub second-order
311: notation\sub extension of
311: polynomials\sub Stirling
311: second-order harmonic numbers
312--313: sums\sub of harmonic numbers
312: Euler\sub identity for continuants
312: Lucas\sub numbers
312: continuants\sub Euler's identity for
312: falling factorial powers\sub related to rising powers
312: harmonic numbers\sub sums using summation by parts
312: recurrences\sub unfolding
312: repertoire method\sub for Fibonacci-like recurrences
312: rising factorial powers\sub related to falling powers
312: rubber band
312: tangent numbers
312: unfolding a recurrence
312: worm\sub on rubber band
313: Eulerian numbers\sub generalized
313: Gau{\ss} (= Gauss)\sub trick
313: bricks
313: harmonic numbers\sub sums of
313: indefinite summation\sub of binomial coefficients
313: stacking bricks
314: Cassini\sub identity, converse
314: continuants\sub zero parameters in
314: harmonic numbers\sub divisibility of
314: permutations\sub excedances in
314: permutations\sub left-to-right maxima in
314: repertoire method\sub for Fibonacci-like recurrences
314~(exercise~46): pentagon
315: Bernoulli numbers\sub denominators of
315: binomial coefficients\sub wraparound
316: Euler\sub triangle
316: Eulerian numbers
316: Lucas\sub numbers
316: Stirling numbers\sub generalized
316: excedances
316: factorial function\sub generalized to nonintegers
316: generalized Stirling numbers
316: generalized factorial function
316: harmonic numbers\sub complex
316: harmonic numbers\sub sums of
316: left-to-right maxima
316: sums\sub of harmonic numbers
317: Catalan numbers\sub in sums
317: Fibonacci\sub addition
317: Stirling numbers\sub identities for
317: Stirling\sub polynomials
317: closed form\sub for generating functions
317: cotangent function
317: paradoxes\sub chessboard
317: polynomials\sub Stirling
317: secant numbers
317: tangent function
317: tangent numbers
317: trigonometric functions\sub related to Bernoulli numbers
317~(exercise~76): Stirling numbers\sub related to Bernoulli numbers
318--319: continuants\sub and matrices
318: Fibonacci\sub number system
318: Fibonomial coefficients
318: binomial coefficients\sub generalized
318: generalized binomial coefficients
318: number system\sub Fibonacci
319: Euler\sub constant ($\approx0.57722$)
319: Gosper-Zeilberger algorithm
319: Stern--Brocot tree\sub largest denominators in
319: Stirling numbers\sub generalized
319: continued fractions
319: discrepancy\sub and continued fractions
319: fractions\sub continued
319: generalized Stirling numbers
319: generating functions\sub for spectra
319: harmonic numbers\sub divisibility of
319: least common multiple\sub of $\{1,\ldots,n\}$
319: notation\sub extension of
319: partial quotients\sub and discrepancies
319: spectra\sub generating functions for
319: tridiagonal matrix
320--321: basis of induction
320--321: downward generalization
320--321: empty case\sub for tilings
320--321: generalization\sub downward
320--321: induction\sub basis of
320--321: mathematical induction\sub basis of
320--321: null case\sub for tilings
320--321: small cases
320--327: domino tilings
320--330: counting\sub with generating functions
320--380: generating functions
320: Browning, Elizabeth Barrett
320: dimers and dimes
321: Fibonacci numbers\sub combinatorial interpretations of
321: closed form
321: sums\sub formal
322: commutative law\sub failure of
323: cheating\sub not
324: Morse
324: clich\'es