Selected Mathematical Publications

James A. Sellers 

Sellers, J. A., Congruences Involving Generalized Frobenius Partitions, International Journal of Mathematics and Mathematical Sciences 16, no. 2 (1993), 413–415  (PDF)

Sellers, J. A., Congruences Involving F–Partition Functions, International Journal of Mathematics and Mathematical Sciences 17, no. 1 (1994), 187–188 (PDF)

Sellers, J. A., New Congruences for Generalized Frobenius Partitions with 2 or 3 Colors, Discrete Mathematics 131 (1994), 367–374 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Two Congruences Involving 4–cores, Electronic Journal of Combinatorics 3, no. 2 (1996), Article R10

Sellers, J. A., Recurrences For 2–Colored and 3–Colored F–Partitions, Discrete Mathematics 156 (1996), 303–310 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Some Amazing Facts About 4–cores, Journal of Number Theory 60, no. 1 (1996), 51–69 (PDF)

Hirschhorn, M. D. and Sellers, J. A., On Representations of a Number as a Sum of Three Triangles, Acta Arithmetica 77 (1996), 289–301 (PDF)

Sellers, J. A., On Infinitely Many Odd Nonunitary Abundant Numbers, Mathematics and Computer Education 31, no. 3 (1997), 241–243 (PDF)

Hirschhorn, M. D. and Sellers, J. A., On Representations of a Number as a Sum of Three Squares, Discrete Mathematics 199 (1999), 85–101  (PDF)

Kolitsch, L. W. and Sellers, J. A., Elementary Proofs of Infinitely Many Congruences for 8–Cores, Ramanujan Journal 3, no. 2 (1999), 221–226  (PDF)

Hirschhorn, M. D. and Sellers, J. A., Some Parity Results for 16–Cores, Ramanujan Journal 3, no. 3 (1999), 281–296  (PDF)

Dolph, L., Reynolds, A., and Sellers, J. A., Congruences for a Restricted m–ary Partition Function, Discrete Mathematics 219, no. 1–3 (2000), 265–269 (PDF)

Frey, D., and Sellers, J. A., Jacobsthal Numbers and Alternating Sign Matrices, Journal of Integer Sequences 3, no. 2 (2000), Article 00.2.3

Hirschhorn, M. D., and Sellers, J. A., Some Relations for Partitions into Four Squares, in the Proceedings of the International Workshop on Special Functions, Asymptotics, Harmonic Analysis, and Mathematical Physics, City University of Hong Kong, June 21–25, 1999, published November 2000 by World Scientific, 118–124 (PDF)

Rodseth, O, and Sellers, J. A., On m–ary Partition Function Congruences: A Fresh Look at a Past Problem, Journal of Number Theory 87, no. 2 (2001), 270–281 (PDF)

Frey, D. and Sellers, J. A., Generalizing Bailey’s Generalization of the Catalan Numbers, Fibonacci Quarterly 39, no. 2 (May 2001), 142–148 (PDF)

Frey, D., and Sellers, J. A, On Powers of 2 Dividing the Values of Certain Plane Partition Functions, Journal of Integer Sequences 4, no. 1 (2001), Article 01.1.8

Eichhorn, D., and Sellers, J. A., Computational Proofs of Congruences for 2–Colored Frobenius Partitions, International Journal of Mathematics and Mathematical Sciences 29, no. 6 (2002), 333–340 (PDF)

Rodseth, O, and Sellers, J. A., Binary Partitions Revisited, Journal of Combinatorial Theory, Series A 98 (2002), 33–45 (PDF)

Sellers, J. A., Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences 5, no. 1 (2002), Article 02.1.2

Sellers, J. A., Beyond Mere Convergence,  PRIMUS (Problems, Resources, and Issues in Mathematics Undergraduate Studies), XII, no. 2 (2002), 157–164 (PDF)

Sellers, J.A., and Williams, H. C., On the Infinitude of Composite NSW Numbers, Fibonacci Quarterly 40, no. 3 (2002), 253–254 (PDF)

Frank, D., Savage, C. D., and Sellers, J. A., On the Number of Graphical Forest Partitions, Ars Combinatoria 65 (2002), 33–37 (PDF)

Sellers, J. A., Extending a Recent Result of Santos on Partitions into Odd Parts, INTEGERS 3 (2003), Article A4

Sellers, J. A., Parity Results for p–Regular Partitions with Distinct Parts, Ars Combinatoria 69 (2003), 143–146 (PDF)

Benjamin, A., Neer, J., Otero, D., and Sellers, J. A., A Probabilistic View of Certain Weighted Fibonacci Sums, Fibonacci Quarterly 41, no. 4 (2003), 360–364 (PDF)

Sellers, J. A., Infinitely Many Composite NSW Numbers:  An Inductive Proof, Missouri Journal of Mathematical Sciences 16, no. 1 (2004) (PDF)

Frey, D., and Sellers, J. A., Prime Power Divisors of the Number of n x n Alternating Sign Matrices, Ars Combinatoria 71 (2004), 139–147 (PDF)

Courtright, K. M. and Sellers, J. A., Arithmetic Properties for Hyper m–ary Partitions, INTEGERS 4 (2004), Article A6

Sellers, J. A., Partitions Excluding Specific Polygonal Numbers as Parts, Journal of Integer Sequences 7, no. 2 (2004), Article 04.2.4

Sellers, J. A., Sills, D. V., and Mullen, G. L., Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy, Electronic Journal of Combinatorics 11, no. 1 (2004), Article R43

Hirschhorn, M. D. and Sellers, J. A., A Different View of m–ary Partitions, Australasian Journal of Combinatorics 30 (2004), 193-196 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Partitions into Three Triangular Numbers, Australasian Journal of Combinatorics 30 (2004), 307-318 (PDF)

Hirschhorn, M. D. and Sellers, J. A., On a Problem of Lehmer on Partitions into Squares, Ramanujan Journal 8, no. 3 (2004), 279-288 (PDF)

Rodseth, O., Sellers, J. A., and Courtright, K. M., Arithmetic Properties of Non-Squashing Partitions into Distinct Parts, Annals of Combinatorics 8, no. 3 (2004), 347-353 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Arithmetic Properties for Overpartitions, Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC) 53 (2005), 65-73 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Further Results for Partitions into Four Squares of Equal Parity, Ars Combinatoria 76 (2005), 33-45 (PDF)

Rodseth, O. and Sellers, J. A., On m–ary Overpartitions, Annals of Combinatorics 9 (2005), 345-353 (PDF)

Hirschhorn, M. D. and Sellers, J. A., An Infinite Family of Overpartition Congruences Modulo 12, INTEGERS 5 (2005), Article A20

Cooper, S., Hirschhorn, M. D., and Sellers, J. A., Partitions into Four Squares, Proceedings of the Jangjeon Mathematical Society 8, no. 1 (2005), 73-94 (PDF)

Rodseth, O. and Sellers, J. A., On a Restricted m-Non-Squashing Partition Function, Journal of Integer Sequences 8, no. 5 (2005), Article 05.5.4

Frey, D. and Sellers, J. A., Arithmetic Properties for a Certain Family of Knot Diagrams, Ars Combinatoria 77 (2005), 65-73 (PDF)

Rodseth, O. and Sellers, J. A., Improving Calculations of the Number of Distinct Alignments of Two Strings, Journal of Quantitative Linguistics 13, no. 1 (2006), 45-55 (PDF)

Rodseth, O. and Sellers, J. A., Partitions With Parts in a Finite Set, International Journal of Number Theory 2, no. 3 (2006), 455-468 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Arithmetic Properties of Overpartitions into Odd Parts, Annals of Combinatorics 10, no. 3 (2006), 353-367 (PDF)

Andrews, G. E. and Sellers, J. A., On Sloane's Generalization of Non-Squashing Stacks of Boxes, Discrete Mathematics 307, no. 9-10 (2007), 1185-1190 (PDF)

Hirschhorn, M. D. and Sellers, J. A., On Recent Congruence Results of Andrews and Paule for Broken k-Diamonds, Bulletin of the Australian Mathematical Society 75 (2007), 121-126 (PDF)

Sellers, J. A., Observations on the Parity of the Total Number of Parts in Odd-Part Partitions, INTEGERS 7 (2007), Article A35

Hopkins, B. and Sellers, J. A., Exact Enumeration of Garden of Eden Partitions, INTEGERS 7, no. 2 (2007), Article A19

Benjamin, A. T., Quinn, J. J., Sellers, J. A., and Shattuck, M., Paint it Black – A Combinatorial Yawp, Mathematics Magazine 81, no. 1 (2008), 45-50 (PDF)

Downey, L., Ong, B. W., and Sellers, J. A., Beyond the Basel Problem: Sums of Reciprocals of Figurate Numbers, The College Mathematics Journal 39, no. 5 (2008), 390-394 (PDF)

Benjamin, A. T., Plott, S., and Sellers, J. A., Tiling Proofs of Recent Sum Identities Involving Pell Numbers, Annals of Combinatorics 12 (2008), 271-278 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Enumerating Unigraphical Partitions, Journal of Integer Sequences 11, no. 4 (2008), Article 08.4.6

Sellers, J. A., A Different Look at Albrecht and White's Path Counting in Grids, Australian Mathematical Society Gazette 36, no. 1 (2009), 47-49 (PDF)

Rodseth, O., Sellers, J. A., and Tverberg, H., Enumeration of the Degree Sequences of Non-Separable Graphs and Connected Graphs, European Journal of Combinatorics 30 (2009), 1301-1317 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Elementary Proofs of Various Facts about 3–cores, Bulletin of the Australian Mathematical Society 79 (2009), 507-512 (PDF)

Hou, X., Mullen, G. L., Sellers, J. A., and Yucas, J. L., Reversed Dickson Polynomials Over Finite Fields, Finite Fields and Their Applications 15, no. 6 (2009), 748-773 (PDF)

Radu, S. and Sellers, J. A., Congruences Modulo Squares of Primes for Fu's k Dots Bracelet Partitions,  International Journal of Number Theory 9, no. 4 (2013), 939–943 (PDF)

Radu, S. and Sellers, J. A., Infinitely Many Congruences for Broken 2-Diamond Partitions Modulo 3, Journal of Combinatorics and Number Theory 4, no. 3 (2013), 195–200  (PDF)

Radu, S. and Sellers, J. A., An Extensive Analysis of the Parity of Broken 3-Diamond Partitions,  Journal of Number Theory 133, no. 11 (2013), 3703–3716 (PDF)

Bessenrodt, C., Olsson, J. B., and Sellers, J. A., Unique Path Partitions: Characterization and Congruences,  Annals of Combinatorics 17 (2013), 591–602 (PDF)

Sellers, J. A., An Unexpected Congruence Modulo 5 for 4-Colored Generalized Frobenius Partitions, Journal of Indian Mathematical Society, Special Volume to Commemorate the 125th Birth Anniversary of Srinivasa Ramanujan (2013), 97–103 (PDF)

Garvan, F. G. and Sellers, J. A., Congruences for Generalized Frobenius Partitions with an Arbitrarily Large Number of Colors, INTEGERS 14 (2014), Article A7 (PDF)

Kursungoz, K. and Sellers, J. A., Variations on a Result of Bressoud, Annals of Combinatorics 18, no. 1 (2014), 117–126 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Arithmetic Properties of 1-shell Totally Symmetric Plane Partitions, Bulletin of the Australian Mathematical Society 89 (2014), 473–478 (PDF)

Fu, S. and Sellers, J. A., Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao, Electronic Journal of Combinatorics 21, no. 2 (2014), Article P2.41

Sellers, J. A., Elementary Proofs of Congruences for the Cubic and Overcubic Partition Functions, Australasian Journal of Combinatorics 60, no. 2 (2014), 191–197 (PDF kindly supplied by AJC)

Hirschhorn, M. D. and Sellers, J. A., A Congruence Modulo 3 for Partitions into Distinct Non–Multiples of Four, Journal of Integer Sequences 17 (2014), Article 14.9.6 (PDF)

Munagi, A. O. and Sellers, J. A., Refining Overlined Parts in Overpartitions via Residue Class:  Bijections, Generating Functions, and Congruences, Utilitas Mathematica 95 (2014), 33–49 (PDF)

Lan, B. and Sellers, J. A., Properties of a Restricted Binary Partition Function a la Andrews and Lewis, INTEGERS 15 (2015), Article A23

Helou, C. and Sellers, J. A., Evaluation of a Family of Binomial Determinants,  Electronic Journal of Linear Algebra 30 (2015), 312–321 (PDF)

Chen, S.-C., Hirschhorn, M. D., and Sellers, J. A., Arithmetic Properties of Andrews’ Singular Overpartitions, International Journal of Number Theory 11, no. 5 (2015), 1463–1476 (PDF)     

Munagi, A. O. and Sellers, J. A., Some Inplace Identities for Integer Compositions, Quaestiones Mathematicae 38, no. 4 (2015), 535–540 (PDF) 

Andrews, G. E., Fraenkel, A. S., and Sellers, J. A., Characterizing the Number of m-ary Partitions Modulo m, American Mathematical Monthly 122, no. 9 (2015), 880–885 (PDF)

Andrews, G. E., Fraenkel, A. S., and Sellers, J. A., m–ary Partitions With No Gaps: A Characterization Modulo m, Discrete Mathematics 339, no. 1 (2016), 283–287 (PDF)

Andrews, G. E. and Sellers, J. A., Congruences for the Fishburn Numbers, Journal of Number Theory 161 (2016), 298–310 (PDF)

Nath, R. and Sellers, J. A., A Combinatorial Proof of the Relationship Between Maximal (2k-1,2k+1)-cores and (2k-1,2k,2k+1)-cores, Electronic Journal of Combinatorics 23, no. 1 (2016), Article P1.13

Mizuhara, M., Sellers, J. A., and Swisher, H., A Periodic Approach to Plane Partition Congruences, INTEGERS 16 (2016), Article A16 (PDF)

Hirschhorn, M. D. and Sellers, J. A., Infinitely Many Congruences Modulo 5 for 4-Colored Frobenius Partitions, Ramanujan Journal 40 (2016), 193–200 (PDF)

Alanazi, A. M., Munagi, A. O. and Sellers, J. A., An Infinite Family of Congruences for l-regular Overpartitions, INTEGERS 16 (2016), Article A37 (PDF)  

Nath, R. and Sellers, J. A., Congruences for Spin Characters of the Double Covers of the Symmetric and Alternating Groups, Advances in Applied Mathematics 80 (2016), 114–130 (PDF)

Nath, R. and Sellers, J. A., Abaci Structures of (s, ms±1)-Core Partitions, Electronic Journal of Combinatorics 24, no. 1 (2017), Article P1.5

Andrews, G. E., Passary, D., Sellers, J. A., and Yee, A. J., Congruences Related to the Ramanujan/Watson Mock Theta Functions ω(q) and υ(q), Ramanujan Journal 43, no. 2 (2017), 347–357 (PDF)

Andrews, G. E., Brietzke, E., Rødseth, Ø. and Sellers, J. A., Arithmetic Properties of m–ary Partitions Without Gaps, Annals of Combinatorics 21, no. 4 (2017), 495–506 (PDF)     

Munagi, A. O. and Sellers, J. A., Generalizing Identities for Inplace Integer Compositions, Quaestiones Mathematicae 41, no. 1 (2018), 41–48 (PDF)

Gu, C., Hirschhorn, M. D., Sellers, J. A., and Xia, E. X. W., Infinite Families of Congruences Modulo 5 and 9 for Overpartitions, Bulletin of the Polish Academy of Sciences Mathematics 61, no. 1 (2018), 31-44 (PDF)

Liu, E. H., Sellers, J. A., and Xia, E. X. W., Congruences Modulo 11 for Broken 5-Diamond Partitions, Ramanujan Journal 46, no. 1 (2018), 151–159 (PDF)

Flowers, T. B., Neville, S., and Sellers, J. A., An m-ary Partition Generalization of a Past Putnam Problem, Australasian Journal of Combinatorics 72, no. 2 (2018), 369–375 (PDF kindly supplied by AJC)

Hirschhorn, M. D. and Sellers, J. A., Parity Results for Partitions Wherein Each Part Appears an Odd Number of Times, Bulletin of the Australian Mathematical Society 99, no. 1 (2019), 51–55 (PDF)

Benjamin, A. T., Crouch, J. and Sellers, J. A., Unified Tiling Proofs of a Family of Fibonacci Identities, Fibonacci Quarterly 57, no. 1 (2019), 29–31 (PDF - full text available at https://www.fq.math.ca/57-1.html)

Brietzke, E. H. M., da Silva, R., and Sellers, J. A., Congruences Related to an Eighth Order Mock Theta Function of Gordon and McIntosh, Journal of Mathematical Analysis and Applications 479, no. 1 (2019), 62–89 (PDF)

da Silva, R., Hopkins, B., and Sellers, J. A., Garden of Eden States in Austrian Solitaire, European Journal of Combinatorics 83 (2020), Article 103023 (PDF)

da Silva, R. and Sellers, J. A., New Congruences for 3-Regular Partitions with Designated Summands, INTEGERS 20A (2020), Article A6    

da Silva, R. and Sellers, J. A, Infinite Families of Congruences for k-Regular Partitions with Designated Summands, Bulletin of the Brazilian Mathematical Society 51 (2020), 357–370 (PDF)

da Silva, R. and Sellers, J. A, Parity Considerations for Mex-Related Partition Functions of Andrews and Newman, Journal of Integer Sequences 23, no. 5 (2020), Article 20.5.7 (PDF)

Hopkins, B. and Sellers, J. A., Turning the Partition Crank, American Mathematical Monthly 127 (2020), 654–657

Hirschhorn, M. D. and Sellers, J. A., Congruences for Overpartitions with Restricted Odd Differences, Ramanujan Journal 53, no. 1 (2020), 167–180 (PDF)

Sellers, J. A., and Zanello, F., On the Parity of the Number of Partitions with Odd Multiplicities, International Journal of Number Theory 17, no. 7 (2021), 1717–1728 (PDF)

Schneider, R., Sellers, J. A., and Wagner, I., Sequentially Congruent Partitions and Partitions into Squares,  Ramanujan Journal  56, no. 2 (2021), 645–650 (PDF)

da Silva, R. and Sellers, J. A., Arithmetic Properties of 3-Regular Partitions in Three Colors, Bulletin of the Australian Mathematical Society 104, no. 3 (2021), 415–423 (PDF)

Gramain, J.-B., Nath, R., and Sellers, J. A., Simultaneous Core Partitions with Common Divisor, Ramanujan Journal  56, no. 3 (2021), 839–863  (PDF)

Hopkins, B., Sellers, J. A., and Stanton, D. W., Dyson’s Crank and the Mex of Integer Partitions, Journal of Combinatorial Theory, Series A 185 (2022), Article 105523  (PDF)

Hopkins, B., Sellers, J. A., and Yee, A. J., Combinatorial Perspectives on the Crank and Mex Partition Statistics, Electronic Journal of Combinatorics 29, no. 2 (2022), Article P2.11 (PDF)

da Silva, R. and Sellers, J. A., Congruences for the Coefficients of the Gordon and McIntosh Mock Theta Function ξ(q), Ramanujan Journal 58, no. 3 (2022), 815–834 (PDF)

da Silva, R., Hirschhorn, M. D., and Sellers, J. A., Elementary Proofs of Infinitely Many Congruences for k-elongated Partition Diamonds, Discrete Mathematics 345, no. 11 (2022), Article 113021 (PDF)

Andrews, G. E., Sellers, J. A. and Soufan, M. F., On the Parity of the Generalized Frobenius Partition Functions φ_k(n), Bulletin of the Australian Mathematical Society  106, no. 3 (2022), 431–436 (PDF)

Petersen, K. L. and Sellers, J. A., Partitions Associated to Class Groups of Imaginary Quadratic Number Fields, Aequationes Mathematicae 97, no. 1 (2023), 63–74 (PDF)

Fulghesu, D., Sellers, J. A., and Taylor, C. K., Infinite Families of Infinite Series with Integer Sums, College Mathematics Journal 54, no. 1 (2023), 33–43 (PDF)

da Silva, R. and Sellers, J. A., Congruences for 3-core Cubic Partitions, Indian Journal of Pure and Applied Mathematics 54 (2023), 404–420 (PDF)

da Silva, R. and Sellers, J. A., Elementary Proofs of Infinite Families of Congruences for Merca's Cubic Partitions, Ramanujan Journal 62, no. 4 (2023), 925–933 (PDF)

Sellers, J. A., An Elementary Proof of a Conjecture of Saikia on Congruences for t-Colored Overpartitions, Boletín de la Sociedad Matemática Mexicana 30 (2024), Article 2 (PDF)

Sellers, J. A. and Smoot, N. A., On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8, International Journal of Number Theory 20, no. 1 (2024), 267–282 (PDF)

Sellers, J. A., New Infinite Families of Congruences Modulo Powers of 2 for 2–Regular Partitions with Designated Summands, INTEGERS 24 (2024), Article A16 (PDF)

Hopkins, B. and Sellers, J. A., On Blecher and Knopfmacher’s Fixed Points for Integer Partitions, Discrete Mathematics 347, no. 5 (2024), Article 113938 (PDF)

Sellers, J. A., Elementary Proofs of Congruences for POND and PEND Partitions, Journal of Integer Sequences 27 (2024), Article 24.4.7 (PDF)

Chern, S. and Sellers, J. A., An Infinite Family of Internal Congruences Modulo Powers of 2 for Partitions into Odd Parts with Designated Summands, to appear in Acta Arithmetica (PDF)

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