Biography
Secretary, American Mathematical Society 2013-2021.
Research Interests: Combinatorics, combinatorial algorithms, network algorithms, graph theory and discrete mathematics, enumeration and structure in combinatorial families; theory of partitions; linear Diophantine enumeration; lattice point enumeration; permutation statistics; the combinatorics, geometry, and number theory of lecture hall partitions.
Interview with Carla D. Savage, by Toufik Mansour for Enumerative Combinatorics and Applications 2:3 (2022) Interview S3I9.
Research Areas
- Algorithms and Theory of Computation
Education
PhD 1977 Mathematics, University of Illinois, Urbana-Champaign
MS 1975 Mathematics, University of Illinois, Urbana-Champaign
BS 1973 Mathematics, Case Western Reserve University
Awards
- Fellow, Society for Industrial and Applied Mathematics (SIAM) - 2019
- Fellow, American Mathematical Society (AMS) - 2012
Publications
See:
-- MathSciNet (Mathematics)-- Google Scholar (Mathematics and Computer Science)
Surveys
The mathematics of lecture hall partitions C. D. Savage
Journal of Combinatorial Theory, Series A, vol. 144 (Nov. 2016) 443-475.
A survey of combinatorial Gray codes
C. D. Savage,
SIAM Review 39 , (1997), no. 4 605-629.
(See Torsten Mutze's 2022 update here)
Papers
Partitions With Constrained Ranks and Lattice Paths
Sylvie Corteel, Sergi Elizalde, and Carla D. Savage
preprint, November 2022.
Coefficients of the inflated Eulerian polynomial
Juan S. Auli, Ron Graham, and Carla D. Savage
Revista Colombiana de Matematicas, to appear.
M. A. Martinez and C. D. Savage,
Journal of Integer Sequences , Vol. 21 (2018), Issue 2, Article 18.2.2.
Lecture hall partitions and the affine hyperoctahedral group
C. R. H. Hanusa and C. D. Savage,
Electronic Journal of Combinatorics, Vol. 25, (2018), Issue 1, Article P1.32
The Mathematics of lecture hall partitions
C. D. Savage
Journal of Combinatorial Theory, Series A, vol. 144 (Nov. 2016) 443-475.
Generating functions and triangulations for lecture hall cones
M. Beck, B. Braun, M. Köppe, C. D. Savage, and Z. Zafeirakopoulos
SIAM J. Discrete Math, vol.30, no. 3 (2016), 1470-1479.
Patterns in inversion sequences I
S. Corteel, M. A. Martinez, C. D. Savage, and M. Weselcouch,
Discrete Mathematics and Theoretical Computer Science, vol. 18, no. 2 (2016)
Permutation Patterns 2015, electronic.
Anti-Lecture Hall Compositions and Andrews' generalization of the Watson-Whipple transformation
C. Corteel, J. Lovejoy, and C. D. Savage,
Journal of Combinatorial Theory, Series A, 134 (2015), 188-195.
s-Lecture hall partitions, self-reciprocal polynomials, and Gorenstein cones
M. Beck, B, Braun, M. Koeppe, C. D. Savage, and Z. Zafeirakopoulos,
Ramanujan Journal,, 36 (2015), no. 1-2, 123-147.
The s-Eulerian polynomials have only real roots
C. D. Savage and M. Visontai,
Transactions of the American Mathematical Society, 367, No. 2, (2015), 1441-1466.
The Eulerian polynomials of type D have only real roots
C. D. Savage and M. Visontai,
FPSAC 2013 , Paris.
Hypergeometric identities associated with statistics on words
G. E. Andrews, C. D. Savage and H. S. Wilf,
Advances in Combinatorics , Proceedings of the Waterloo Workshop on Computer Algebra - W80,
I. S. Kotsireas and E. V. Zima, eds., Springer (2013) 77-100.
Lattice point generating functions and symmetric cones
M. Beck, T. Bliem, B. Braun, and C. D. Savage,
Journal of Algebraic Combinatorics, Vol. 38, Issue 3 (2013) 543-566.
Rational lecture hall polytopes and inflated Eulerian polynomials
T. W. Pensyl and C. D. Savage,
Ramanujan Journal, Vol. 31 (2013) 97-114.
Lecture hall partitions and the wreath products C_k \wr S_n
T. W. Pensyl and C. D. Savage,
Integers, 12B, #A10 (2012/13).
The 1/k -Eulerian Polynomials
C. D. Savage and G. Viswanathan,
The Electronic Journal of Combinatorics, Vol. 19 (2012) Research Paper P9 , 21 pp. (electronic).
Ehrhart series of lecture hall polytopes and Eulerian polynomials for inversion sequences,
C. D. Savage and M. J. Schuster,
Journal of Combinatorial Theory, Series A, Vol. 119 (2012) 850-870.
Lecture hall sequences, q-series, and asymmetric partition identities
S. Corteel, C. D. Savage, and A. V. Sills,
in Partitions, q-series, and Modular Forms,
Developments in Mathematics, vol. 23, Krishnaswami Alladi and Frank Garvan, eds., Springer (2012) 53-68.
Mahonian pairs,
B. E. Sagan and C. D. Savage,
Journal of Combinatorial Theory, Series A 119 (2012) 526-545.
On an identity of Gessel and Stanton and the new little G\"ollnitz identities
C. D. Savage and A. V. Sills
Advances in Applied Mathematics, 46 (2011) 563-575.
The geometry of lecture hall partitions and quadratic permutation statistics
K. L. Bright and C. D. Savage,
Discrete Mathematics and Theoretical Computer Science Proceedings,
22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), San Francisco, August 2010, 569-580.
Combinatorial interpretations of binomial coefficient analogues related to Lucas sequences
B. E. Sagan and C. D. Savage,
Integers, Vol. 10 (2010) A52, 697-703.
Generalizing the combinatorics of binomial coefficients via l-nomials
N. Loehr and C. D. Savage,
Integers, Vol. 10 (2010) A45, 531-558.
Symmetrically constrained compositions
M. Beck, I. M. Gessel, S. Lee, and C. D. Savage,
Ramanujan Journal, Vol. 23 (2010) 355-369.
On q-series Identities Arising from Lecture Hall Partitions.
G. E. Andrews, S. Corteel, and C. D. Savage,
International Journal of Number Theory, Volume 5, No. 1 (2009) 1-11.
An update on the middle levels problem
I. Shields, B. J. Shields, and C. D. Savage,
Discrete Mathematics, 309 (2009), 5271-5277
On the existence of summetric chain decompositions in a quotient of the Boolean lattice
Z. Jiang and C. D. Savage,
Discrete Mathematics, 309 (2009), 5278-5283
Minimizing Transceivers in Optical Path Networks
P. Iyer, R. Dutta, and C. D. Savage,
Journal of Optical Networks, Vol. 8 (2009) 454-461.
Enumeration of Integer Solutions to Linear Inequalities Defined by Digraphs
J. W. Davis, E. D'Souza, S. Lee, and C. D. Savage,
Contemporary Mathematics, Vol. 452 (2008) 79-91.
Let me tell you my favorite lattice-point problem
M. Beck, B. Nill, B. Reznick, C. Savage, I. Soprunov, and Z. Xu,
Contemporary Mathematics, Vol. 452 (2008) 179-187.
Euler's partition theorem and the combinatorics of l-sequences.
C. D. Savage and A. J. Yee,
Journal of Combinatorial Theory, Series A, Volume 155, No. 6 (2008) 967-996.
The joint distribution of descent and major index over restricted sets of permutations.
S. Corteel, I. M. Gessel, C. D. Savage, and H. S. Wilf,
Annals of Combinatorics, 11 (2007), no. 3-4, 375-386.
Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems
S. Corteel, S. Lee, and C. D. Savage,
in Combinatorial Number Theory, de Gruyter, Berlin (2007), 131-155.
The Search for Simple Symmetric Venn Diagrams
F. Ruskey, C. D. Savage, and S. Wagon,
Notices of the American Mathematical Society, Vol. 53, No. 11, (2006), 1304-1311.
Pattern avoidance in compositions and multiset permutations,
C. D. Savage and H. S. Wilf,
Advances in Applied Mathematics, Vol. 36, Issue 2, (Feb. 2006) 194-201.
(Presented at the The Third International Conference on Permutation Patterns, University of Florida, Gainesville, March 2005.)
Enumeration of Sequences Constrained by the Ratio of Consecutive Parts,
S. Corteel, S. Lee, and C. D. Savage,
S\'eminaire Lotharingien de Combinatoire 54A (2005), Art. B54Aa,12pp. (electronic).
A Note on Partitions and Compositions Defined by Inequalities,
S. Corteel, C. D. Savage, and H. S. Wilf,
Integers, 5(1), A24, (2005), 11pp. (electronic).
Common Intervals of Trees ,
S. Heber and C. D. Savage,
Information Processing Letters , Vol. 93, Issue 2 (2005) 69-74.
Partitions and compositions defined by inequalities ,
S. Corteel and C. D. Savage,
Ramanujan Journal , Vol. 8, No. 3(2004) 357-381.
Partitions and compositions defined by (in)equalities (Extended Abstract) ,
in Fourteenth International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'02), Melbourne, July 2002.
On the multiplicity of parts in a random composition of a large integer,
P. Hitczenko and C. D. Savage,
SIAM Journal on Discrete Mathematics, Vol. 18, No. 2 (2004) 418-435.
Regularly spaced subsums of integer partitions,
E. R. Canfield, C. D. Savage, H. S. Wilf,
Acta Arithmetica 115, no. 3 (2004) 205-216.
Lecture hall theorems, q-series, and truncated objects,
S. Corteel and C. D. Savage,
Journal of Combinatorial Theory, Series A 108, no. 2 (2004) 217-245.
Half-Simple Symmetric Venn Diagrams,
C. E. Killian, F. Ruskey, C. D. Savage, and M. Weston,
Electronic Journal of Combinatorics 11 (2004), Research Paper 86, 22 pp. (electronic).
Venn diagrams and symmetric chain decompositions in the Boolean Lattice ,
J. Griggs, C. E. Killian and C. D. Savage,
Electronic Journal of Combinatorics 11 (2004), Research Paper 2, 30 pp. (electronic).
Antipodal Gray codes ,
C. E. Killian and C. D. Savage,
Discrete Mathematics Vol. 281, Nos. 1-3 (2004) 221-236.
A Note on Hamilton Cycles in Kneser Graphs ,
I. Shields and C. D. Savage,
Bulletin of the Institute for Combinatorics and Its Applications , Vol. 40 (2004) 13-22.
Plane Partition Diamonds and Generalizations ,
S. Corteel and C. D. Savage,
Integers 3, A9, (2003) 8pp. (electronic).
Anti-lecture hall compositions ,
S. Corteel and C. D. Savage,
Discrete Mathematics , Vol. 263, Nos. 1-3 (2003) 275-280.
On the existence of Hamiltonian paths in the Cover Graph of M(n) ,
C. D. Savage, I. Shields, and D. B. West,
Discrete Mathematics, Vol. 262, Nos. 1-3 (2003) 241-252.
On the number of graphical forest partitions,
D. A. Frank, C. D. Savage, and J. A. Sellers,
Ars Combinatoria , Vol. 65 (2002) 33-37.
A Generatingfunctionology Approach to a Problem of Wilf ,
P. Hitczenko, Cecil Rousseau, and C. D. Savage,
Journal of Computational and Applied Mathematics , Vol. 142, No. 1 (2002) 107-114.
A lattice path approach to counting partitions with minimum rank t ,
A. Burstein, S. Corteel, A. Postnikov, and C. D. Savage,
Discrete Mathematics , Vol. 249, Nos. 1-3 (2002) 31-39.
On multicolor partitions and generalized Rogers-Ramanujan identities ,
N. Jing, K. C. Misra, and C. D. Savage,
Communications in Contemporary Mathematics , Vol. 3, No. 4 (2001) 533-548.
On the probability that a randomly chosen part size in a random composition is unrepeated,
P. Hitczenko and C. D. Savage,
Paul Erdos and his mathematics , (Budapest, 1999), 108--111, Janos Bolyai Math. Soc., Budapest, 1999.
A Hamilton path heuristic with applications to the middle two levels problem ,
I. Shields and C. D. Savage,
Congressus Numerantium , Vol 140 (1999) 161-178.
On the multiplicity of parts in a random partition,
S. Corteel, B. G. Pittel, C. D. Savage, and H. S. Wilf,
Random Structures and Algorithms 14, (1999), no. 2, 185-197.
Combinatorial families that are exponentially far from being listable in Gray code sequence ,
T. Chinburg, C. D. Savage, and H. S. Wilf,
Transactions of the American Mathematical Society 351 , (1999), no. 1, 379-402.
A bijection for partitions with all ranks at least t,
S. Corteel, C. D. Savage, and R. Venkatraman,
Journal of Combinatorial Theory, Series A 83, No. 2 (1998) 202-220.
Extended Abstract
in Tenth International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'98), Toronto, June 1998, 179-192.
A pentagonal number sieve,
S. Corteel, C. D. Savage, H. S. Wilf, and D. Zeilberger,
Journal of Combinatorial Theory, Series A 82 , No. 2 (1998) 186-192.
Graphical basis partitions ,
J. M. Nolan, C. D. Savage, V. Sivaraman, and P. Tiwari,
Graphs and Combinatorics 14 , (1998) 241 - 261.
Durfee Polynomials,
S. Corteel, E. R. Canfield, and C. D. Savage,
Electronic Journal of Combinatorics 5(1) , R32 (1998).
Extended abstract
in Ninth International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'97) , Vienna, July 14-18 1997, Volume 1, 142-153.
The connectivity of acyclic orientations graphs ,
C. D. Savage and C.-Q. Zhang,
Discrete Mathematics 184 (1998) no. 1-3, 281-287.
Basis partitions ,
J. M. Nolan, C. D. Savage, and H. S. Wilf,
Discrete Mathematics 179 (1998) no. 1-3, 277-283.
A survey of combinatorial Gray codes ,
C. D. Savage,
SIAM Review 39 , (1997), no. 4 605-629.
Efficient generation of graphical partitions ,
T. Barnes and C. D. Savage,
Discrete Applied Mathematics 78 , (1997), no. 1-3, 17-26.
Balanced Gray Codes,
G. S. Bhat and C. D. Savage,
Electronic Journal of Combinatorics No. 1, R25 (1996).
A Gray code for combinations of a multiset,
F. Ruskey and C. D. Savage,
European Journal of Combinatorics 68, (1996) 1-8.
A Gray code for necklaces of fixed density,
T. M. Wang and C. D. Savage,
SIAM Journal on Discrete Mathematics 9, No. 4 (1996) 654-673. (Figures not included in postscript file.)
A recurrence for counting graphical partitions,
T. M. Barnes and C. D. Savage,
Electronic Journal of Combinatorics 2, R11 (1995).
Gray code enumeration of families of integer partitions,
D. J. Rasmussen, C. D. Savage, and D. West,
Journal of Combinatorial Theory, Series A, 70 no. 2 (1995) 201-229.
Monotone Gray codes and the middle two levels problem,
C. D. Savage and P. Winkler,
Journal of Combinatorial Theory, Series A 70, 2 (1995) 230-248.
Gray codes for set partitions and restricted growth tails
F. Ruskey and C. D. Savage,
Australasian Journal of Combinatorics 10 (1994) 85-96.
Hamilton-connected derangement graphs on S_n,
D. J. Rasmussen and C. D. Savage,
Discrete Mathematics 133 (1994) 217-223. (Some figures incomplete in postscript file.)
Gray code results for acyclic orientations,
C. D. Savage, M. B. Squire, and D. B. West,
Congressus Numerantium 96 (1993) 185-204.
Long cycles in the middle two levels of the Boolean lattice,
C. D. Savage,
Ars Combinatoria 35-A (1993) 97-108.
Hamilton cycles that extend transposition matchings in Cayley graphs of $S_n$,
F. Ruskey and C. D. Savage,
SIAM Journal on Discrete Mathematics 6, No.1 (1993) 152-166.
Generating necklaces
F. Ruskey, C. D. Savage, and T. M. Wang,
Journal of Algorithms 13 (1992) 414-430.
A new algorithm for generating necklaces,
C. D. Savage, and T. M. Wang,
Proceedings, Twenty-eighth Annual Allerton Conference on Communication, Control, and Computing , Allerton (1992).
Generating permutations with k-differences,
C. D. Savage,
SIAM Journal on Discrete Mathematics 3, No. 4 (1990) 561-573.
Solving combinatorial problems on arrays with one-way data flow,
C. D. Savage, M. F. M. Stallmann, and J. E. Perry,
Algorithmica 5, No. 2 (1990) 179-200.
Gray code sequences of partitions,
C. D. Savage,
Journal of Algorithms 10, No. 4 (1989) 577-595.
Recognizing majority on a one-way mesh,
C. D. Savage,
Information Processing Letters 27 (1988) 221-225.
Systolic arrays with embedded tree structures for connectivity problems,
S. V. Ashtaputre and C. D. Savage,
IEEE Transactions on Computers, Vol. C-34, No. 5, May 1985, 483-484.
A systolic design for connectivity problems,
C. D. Savage,
IEEE Transactions on Computers, Vol. C-33, No. 1, January 1984, 99-104.
Short strings containing all k-element permutations,
C. D. Savage,
Discrete Mathematics, 10, October 1982, 281-285.
Content-addressable read/write memories for image analysis,
W. E. Snyder and C. D. Savage,
IEEE Transactions on Computers, Vol. C-31, No. 10, October 1982, 963-967.
Depth-first search and the vertex cover problem,
C. D. Savage,
Information Processing Letters 14, No. 5, July 1982, 233-235.
Fast, efficient parallel algorithms for some graph problems,
C. D. Savage and J. Ja'Ja',
SIAM Journal on Computing 10, No. 4, November 1982, 682-691.
Maximum matchings and trees,
C. D. Savage,
Information Processing Letters 10, No. 4,5, July 1980, 202-205.
An O(n^2) algorithm for Abelian group isomorphism
C. D. Savage
Technical Report TR 80-01, North Carolina State University, January 1980.