## 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.

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.

*Patterns in inversion sequences II: Inversion sequences avoiding triples of relations*

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.