Publications

Selected publications of H. Wilf

2008
- Extreme palindromes (with Kathy Ji), Amer. Math. Monthly, 115, no. 5 (2008), 447--451.
- The joint distribution of descent and major index over restricted sets of permutations (with S. Corteel, I.M. Gessel, and C.D. Savage) Ann. Comb. 11 (2007), no. 3-4, 375--386.
2007

Closed form summation of C-finite sequences (with Curtis Greene) Transactions Amer. Math. Soc., 359 (2007), 1161-1189.

Here is a Mathematica notebook that does the closed form summation that this paper describes.

Left-to-right maxima in words and multiset permutations (with Amy N. Myers), Israel J. Math., to appear.
Counting permutations by their runs up and down (with E. Rodney Canfield), J. Combinatorial Theory, to appear.
Computing the distribution of the maximum in balls-and-boxes problems, with application to clusters of disease cases (with Warren J. Ewens), Proc. Nat. Acad. Sci. USA 104 (2007), 11189--11191.

2006

BG-ranks and 2-cores (with William Y.C. Chen and Kathy Ji), Electronic J. Combinat. 13 (1), 2006, #N18.

2005

The variance of the Stirling cycle numbers, preprint.
Pattern avoidance in compositions and multiset permutations (with Carla Savage), Adv. Appl. Math. 36 (2006), 194-201

Mathematics: An Experimental Science, Draft of a chapter in the forthcoming volume "The Princeton Companion to Mathematics," edited by Tim Gowers.
A Note on Partitions and Compositions Defined by Inequalities (with Sylvie Corteel and Carla Savage), Integers, Vol. 5(1), 2005, A24.

2004

The method of characteristics, and `problem 89' of Graham, Knuth, and Patashnik. Submitted.
The Redheffer matrix of a partially ordered set, Elec. J. Combinatorics (2) 2004-2005, #R10.

Irreducible compositions and the first return to the origin of a random walk. (with Edward A. Bender, Gregory F. Lawler, and Robin Pemantle) Séminaire Lotharingien de Combinatoire, 50 (2004) #B50h.
The combinatorics of a three-line circulant determinant. Israel J. Math., 143 (2004), 141--156. (with Nicholas A. Loehr and Gregory S. Warrington)
Acyclic Digraphs and Eigenvalues of (0,1)-Matrices. with Brendan D. McKay, Frederique E. Oggier, Gordon F. Royle, N. J. A. Sloane, and Ian M. Wanless, J. Integer Sequences, 7 (2004), #04.3.3.
Regularly spaced subsums of integer partitions. (with E. Rodney Canfield and Carla D. Savage) Acta Arithmetica, 115 (2004), 205--216.

2003

A Discontinuity in the Distribution of Fixed Point Sums. Elec. J. Comb. 10 #R15 (with Edward A. Bender, E. Rodney Canfield, and L. Bruce Richmond)
Some new aspects of the coupon-collector's problem. SIAM Journal on Discrete Mathematics 17, 1--17. (with Amy N. Myers)
The distribution of longest increasing subsequences in pattern-restricted permutations. Elec. J. Comb. 9 #R12.(with Emeric Deutsch and A. J. Hildebrand)
Searching the web, with eigenvectors, The UMAP Journal 23 (2003), no. 2, 101--103.

2002

The distributions of the entries of Young tableaux, with Brendan McKay and Jennifer Morse, J. Combin. Theory Ser. A 97 (2002), no. 1, 117--128.
The patterns of permutations, Discrete Mathematics 257 (2002), 575-583.

2000

Recounting the Rationals (with Neil Calkin), The American Mathematical Monthly 107 (2000), 360--363.
Lectures on Integer Partitions, Pacific Institute for the Mathematical Sciences, June, 2000 (monograph).
Averaging sequences, deranged mappings, and a problem of Lampert and Slater, with Neil Calkin and E. Rodney Canfield, J. Combinatorial Theory Ser. A 91 (2000), 171--190.
Identically distributed pairs of partition statistics, Séminaire Lotharingien Combinatoire 44 (2000), [B44c].

1999

Accelerated series for universal constants by the WZ method, Discrete Mathematics & Theoretical Computer Science 3:4 (1999), 155--158.
The number-theoretic content of the Jacobi triple product identity. The Andrews Festschrift (Maratea, 1998). Sém. Lothar. Combin. 42 (1999), Art. B42k
Permutation patterns and continued fractions (with Aaron Robertson and Doron Zeilberger), Electron. J. Combin.6 (1999), no. 1, #R38
On the multiplicity of parts in a random partition (with S. Corteel, B. Pittel, and C. Savage), Random Structures and Algorithms 14(1999), no. 2, 185--197.
Combinatorial families that are exponentially far from being listable in Gray code sequence (with Ted Chinburg and Carla D. Savage), Trans. Amer. Math. Soc.351 (1999), no. 1, 379--402. (Here is an erratum for this paper.)

1998

On lattice walks and permutations with no long increasing subsequences, . Electron. J. Combin. 5 (1998), R2, 11 pp. (with Ira Gessel and Jonathan Weinstein)
A pentagonal number sieve (with Corteel, Sylvie; Savage, Carla D.; Zeilberger, Doron) J. Combin. Theory Ser. A \textbf{82} (1998), no. 2, 186--192.

The number of independent sets in a grid graph (with Neil Calkin), SIAM J. Discr. Math. 11 (1998), 54-60.
Basis partitions (with Jennifer Nolan and Carla Savage), Discrete Mathematics, 179 (1998), 277-283.

1997

Cyclic strings without long constant blocks (with Alexander Burstein), Fibonacci Quarterly 35 (1997), 240--247.
When can the sum of $(1/p)$th of the binomial coefficients have closed form?(with Marko Petkovšek), Electron. J. Combinat., 4, no. 2 (1997), #R21.
How to do Monthly problems with your computer, The American Mathematical Monthly 104 (June-July, 1997) (with István Nemes, Marko Petkovsek and Doron Zeilberger)

1996

Récents développements et problémes dans le domaine de la génération aléatoire, Theoretical Comp. Sci. 159 (1996), 5-13.
A high-tech proof of the Mills-Robbins-Rumsey determinant identity (with Marko Petkovšek), Electron. J. Combinat.} 3 (1996), no. 2, #R19.
Counting pairs of lattice paths by intersections, (with Wayne Goddard, Walter Shur and Lily Yen), \textit{J. Combin. Theory Ser. A} \textbf{74} (1996), 173--187.
A=B, (with Marko Petkovšek and Doron Zeilberger), A K Peters, Ltd., Wellesley, MA, 1996.

1995

The computer-aided discovery of a theorem about Young tableaux, Symbolic computation in combinatorics $\Delta_1$ (Ithaca, NY, 1993), J. Symbolic Comput. 20 (1995), no. 5-6, 731--735.
Five surprisingly simple complexities, (with Volker Strehl) Symbolic computation in combinatorics $\Delta_1$ (Ithaca, NY, 1993), J. Symbolic Comput. 20} (1995), no. 5-6, 725--729.
The Problem of the Kings, Electron. J. Combinat. 2 (1995), R4.

1990-1994

A combinatorial determinant
The distribution of subset sums modulo m (with Stan Wagon), Elec. J. Combinat. 1 (1994), R3, 15pp.
The rectilinear crossing number of a complete graph and Sylvester's "Four Point Problem" of geometric probability (with Ed Scheinerman) Amer. Math. Monthly 101 (1994), 939-943.
On the coefficients in the Hardy-Ramanujan-Rademacher formula for p(n) (with Gert Almkvist) J. Number Theory (with Gert Almkvist) 1994.
A Footnote On Two Proofs of the Bieberbach-de Branges Theorem Bull. London Math Soc. 26 (1994), 61-63.
The asymptotic behavior of the Stirling numbers of the first kind J. Combinatorial Theory, 64 (1993) 344-349.
Congruence problems involving Stirling numbers of the first kind (with Rhodes Peele and A.J. Radcliffe) Fibonacci Quarterly, 31 (1993), 73-80.
An algorithmic proof theory for hypergeometric (ordinary and ``$q$'') multisum/integral identities (with Doron Zeilberger) Inventiones Mathematicae 108 (1992), 575-633.
The distribution of the binomial coefficients modulo p (with Richard Garfield) J. Number Theory 41 (1992), 1-5.
Ascending subsequences of permutations and the shapes of Young tableaux J. Combinatorial Theory, Ser. A 60 (1992), 155-157.
Rational function certification of multisum/integral "q" identities (with Doron Zeilberger), Bull. Amer. Math. Soc. 27 (1992), 148-153.
Functional iteration and the Josephus problem (with Andrew Odlyzko) Glasgow Math. J., 1991.
Two algorithms for the sieve method, J. Algorithms 12 (1991), 179-182.
Graphical combinatorial families and unique representation of integers, Graph Theory, Combinatorics and Applications, Y. Allavi, G. Chartrand, O. Oellermann, A.J. Schwenk Eds., John Wiley, 1991.
Rational functions certify combinatorial identities (With Doron Zeilberger) Journal of the American Mathematical Society, 3 (1990), 147-158.

1980-1989

The power of a prime that divides a generalized binomial coefficient (with Donald E. Knuth), J. fur die reine u. angew. Math. 396 (1989), 212-219.
Periodicities of partition functions and Stirling numbers modulo p (with Albert Nijenhuis), J. Number Theory 25 (1987), 308-312.
The asymptotics of $e^{P(z)}$ and the number of elements of each order in $S_n$, Research Announcement, Bull. Amer. Math. Soc. 15 (1986), 228-232.
The number of maximal independent sets in a tree, SIAM J. Alg. Discr. Meth. 7 (1986), 125-130.
Spectral bounds for the clique and independence number of a graph, J. Comb. Theory Ser. B 40 (1986), 113-117.
A theoretical analysis of backtracking in the graph coloring problem (with Edward A. Bender), J. Algorithms 6 (1985), 275-282.
Another probabilistic method in the theory of Young tableaux (with Curtis Greene), J. Comb. Theory 37 (1984), 127-135.
Backtrack: An expected O(1) time algorithm for the graph coloring problem, Inf. Proc. Lett. 18 (1984), 119-122.
Three problems in combinatorial asymptotics, J. Comb. Theory Ser. A 35 (1983), 199-207.
Sieve equivalence in generalized partition theory, J. Combinatorial Theory 34 (1983) 80-89.
The disk with the college education, Amer. Math. Monthly 89 (1982), 4-8.
An algorithm-inspired proof of the spectral theorem, Amer. Math. Monthly, 88 (1981), 49-50.
The uniform selection of free trees, J. Algorithms 2 (1981), no. 2, 204-207.

1970-1979

A probabilistic proof of a formula for the number of Young Tableaux of a given shape, Adv. in Math., 31 (1979), 104-109 (with C. Greene and A. Nijenhuis).
A global bisection algorithm for computing the zeroes of polynomials in the complex plane, J. Assoc. Comp. Mach. 25 (1978), 415-420.
A unified setting for selection algorithms, II, Annals of Discrete Mathematics 2: Algorithmic aspects of combinatorics, North Holland (1978), 135-148.
A note on $P(-\lambda ;G)$, J. Combinatorial Theory, 22 (1977).
A unified setting for sequencing, ranking and random selection of combinatorial objects, Advances in Math., 24 (1977), 281-291.
The sequential and random selection of subspaces over a finite field, J. Combinatorial Theory, 22 (1977), 107-109 (with E. Calabi).
Which polynomials are chromatic?, Proc. Rome Conference on Combinatorial Theory, Accademia Nazionale dei Lincei, 1976, Vol. I, 247-256.
A method and two algorithms in the theory of partitions, J. Combinatorial Theory, 18 (1975), 219-222 (with A. Nijenhuis).
On Eulerian circuits and words with prescribed adjacency patterns, J. Combinatorial Theory, 18 (1975), 80-88 (with Joan Hutchinson).
Representations of integers by linear forms in nonnegative integers, J. Number Theory, 4 (1972), 98-106 (with A. Nijenhuis).
On a conjecture of Ryser and Minc, Nederl. Akad. Wetensch. Proc. Ser. A 73 = Indag. Math. 32 (1970), 151--157 (with Albert Nijenhuis).

1960-1969

An inequality for the chromatic number of graph (with George Szekeres), J. Comb. Theory 4 (1968), 1-3.
Hadamard determinants, M\"obius functions, and the chromatic number of a graph, Bull. Amer. Math. Society, 74 (1968), 960-964.
The eigenvalues of a graph and its chromatic number, J. London Math. Soc., 42 (1967), 330-332.
Small eigenvalues of large Hankel matrices, (with H. Widom), Proc. Amer. Math. Soc., 17 (1966), 338-344.
Uniqueness theorems for periodic functions, (with N. Fine), Proc. Amer. Math. Soc., 16 (1965), 109-114.
The interchange graph of a finite graph, (with A. van Rooij), Acta Mathematica (Hung.), 16 (1965), 263-269.
Exactness conditions in numerical quadrature, Numerische Mathematik, 6 (1964), 315-319.
On the zeros of Riesz' function in the analytic theory of numbers, Illinois J. Math., 8 (1964), 639-641.
Dirichlet series and Toeplitz forms, J. Math. Anal. Appl. 8 (1964), 45-51.
Some applications of the inequality of arithmetic and geometric means to polynomial equations, Proc. Amer. Math. Soc., 14 (1963), 263-265.
On Hilbert's inequality in n dimensions, (with N. G. de Bruijn), Bull. Amer. Math. Soc., 68 (1962), 70-73.
Budan's theorem for a class of entire functions Proc. Amer. Math. Soc., 13 (1962), 122-125.
Subordinating factor sequences for convex maps of the unit circle Proc. Amer. Math. Soc., 12 (1961), 689-693.
Perron-Frobenius theory and the zeros of polynomials, Proc. Amer. Math. Soc., 12 (1961), 247-250.
The possibility of Tschebycheff Quadrature on infinite intervals Proc. Nat. Acad. Sci. U.S.A., 47 (1961), 209-213.
A class of linear differential-difference equations, (with M. Slater), Pacific J. Math., 10 (1960), 1419-1427.