023. A Note on the Rado numbers \(R_k(3,c)\)
Tanbir Ahmed, Robert Malo, Daniel Schaal, Submitted to a journal.
Ramsey Theory on the Integers

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022. On the \(3\)-color off-diagonal generalized Schur numbers \(S(3; 2, k_1, k_2)\)
Tanbir Ahmed, Luis Boza, Maria P. Revuelta, and Maria I. Sanz, Submitted to a journal.
Ramsey Theory on the Integers SAT-Solving

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021. On the \(3\)-color off-diagonal generalized Schur numbers \(S(3; 2,2,k)\)
Tanbir Ahmed, Luis Boza, Maria P. Revuelta, and Maria I. Sanz, Submitted to a journal.
Ramsey Theory on the Integers SAT-Solving

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020. Establishing lower bounds and exact values of the \(2\)-color off-diagonal generalized weak Schur numbers \(WS(2; k_1, k_2)\)
Tanbir Ahmed, Luis Boza, Maria P. Revuelta, and Maria I. Sanz, Submitted to a journal.
Ramsey Theory on the Integers SAT-Solving

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019. Lower bounds and exact values of the \(2\)-color off-diagonal generalized weak Schur numbers \(WS(2; k_1, k_2)\) conference
Tanbir Ahmed, Luis Boza, Maria P. Revuelta, and Maria I. Sanz, Procedia Computer Science, 223 (2023), 403-405. XII LAGOS, 2023.
Ramsey Theory on the Integers SAT-Solving

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018. Exact values and lower bounds on the \(n\)-color weak Schur numbers for \(n = 2, 3\). journal
Tanbir Ahmed, Luis Boza, Maria P. Revuelta, and Maria I. Sanz, The Ramanujan Journal, 62 (2) (2023), 347-363. , Open access, (2023).
Ramsey Theory on the Integers SAT-Solving Abstract

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017. Thue-Morse substitution and self similar groups and algebras journal
Laurent Bartholdi, José M. R. Caballero, and Tanbir Ahmed, Algebra and Discrete Mathematics, 34 (1) (2022), 1-14.
Self-Similar Algebra Abstract

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016. A Family of doubly stochastic matrices involving Chebyshev polynomials. journal
Tanbir Ahmed and José M. R. Caballero, Algebra and Discrete Mathematics, 27 (2) (2019), 155-164. MR3982300.
Self-Similar Algebra Abstract

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015. Power Sum Polynomials as Relaxed EGZ Polynomials. journal
Tanbir Ahmed, Arie Bialostocki, Thang Pham, and Le Anh Vinh, Integers 19 (2019), A49. MR4017190.
Zero-Sum Ramsey Theory Abstract

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014. On Generalized Schur Numbers journal
Tanbir Ahmed and Daniel Schaal, Experimental Mathematics, 25 (2) (2016), 213-218. MR3463569. (PDF)
Ramsey Theory on the Integers SAT-Solving Abstract

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013. On Colouring Integers without t-AP distance sets journal
Tanbir Ahmed, Algebra and Discrete Mathematics, 22 (1) (2016), 1-10. MR3573541. (PDF)
Ramsey Theory on the Integers SAT-Solving Abstract

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012. On Distance Sets in the Triangular Lattice journal
Tanbir Ahmed and David Wildstrom, Bull. Inst. Combin. Appl. 75 (2015), 118-127. MR3444619. (PDF)
Combinatorial Geometry Abstract

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011. Remembering Hunter Snevily journal
Tanbir Ahmed, André Kézdy, and Douglas B. West, Bull. Inst. Combin. Appl., 73 (2015), 7-17. MR3331369. (PDF)
Research Memoir

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010. On the van der Waerden numbers \(w(2; 3, t)\) journal
Tanbir Ahmed, Oliver Kullmann, and Hunter Snevily, Discrete Applied Mathematics, 174 (2014), 27-51. MR3215454.
Ramsey Theory on the Integers SAT-Solving Abstract
--- The paper got a citation in D. E. Knuth's Volume 4, Fascicle 6: Chapter on Satisfiability

--- See Wikipedia entry of Van der Waerden numbers for my contributions in that list
--- Recently (2022), Ben Green in New Lower Bounds for van der Waerden Numbers, disproved the much-speculated conjecture \(w(2; 3, k)=\cal{O}(k^2)\) (originally formulated by Ron Graham in around 2004, and subsequently supported with data by others and ourselves) by constructing a red-blue coloring of \(1,2,\ldots,N\) with no blue arithmetic progression of length 3 and no red arithmetic progression of length \(e^{C(\log N)^{3/4}(\log\log N)^{1/4}}\), and consequently showing that \(w(2; 3, k)\) is bounded from below by \(k^{b(k)}\) where \(b(k) = c\left({\log{k}\over\log\log{k}}\right)^{1/3}\). See Erica Klarreich's Quanta Magazine article Mathematician Hurls Structure and Disorder Into Century-Old Problem.

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009. The α-labeling number of comets is 2 journal
Tanbir Ahmed and Hunter Snevily, Bull. Inst. Combin. Appl., 72 (2014), 25-40. (PDF) MR3362514.
Graph Labeling Abstract
--- (See Joseph A. Gallian's A Dynamic Survey of Graph Labeling)

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008. Sparse Distance Sets in the Triangular Lattice journal
Tanbir Ahmed and Hunter Snevily, Electronic Journal of Combinatorics, 20 (4) (2013), P33. MR3158272.
Combinatorial Geometry Abstract

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007. Unique Sequences Containing No k-Term Arithmetic Progressions journal
Tanbir Ahmed, Janusz Dybizbański, and Hunter Snevily, Electronic Journal of Combinatorics, 20 (4) (2013), P29. MR3158268.
Combinatorics Abstract

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006. Some properties of Roller Coaster Permutations journal
Tanbir Ahmed and Hunter Snevily, Bull. Inst. Combin. Appl., 68 (2013), 55-69. (PDF) MR3136863.
Combinatorics Abstract
--- (See Biedl et al., Rollercoasters: long sequences without short runs., SIAM J. Discrete Math. 33, No. 2, 845-861 (2019).
--- (See two conjectures in the Open Problems Garden)
--- (See William Adamczak A Note on the Structure of Roller Coaster Permutations, preprint, May 2016)
--- (See William Adamczak, Jacob Boni Roller Coaster Permutations and Partition Numbers, preprint, March 2017)

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005. Strict Schur Numbers journal
Tanbir Ahmed, Michael G. Eldredge, Jonathan J. Marler, and Hunter Snevily, Integers, 13 (2013). A22. MR3083484.
Ramsey Theory on the Integers Abstract

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004. Some more van der Waerden numbers journal
Tanbir Ahmed, Journal of Integer Sequences, 16 (2013), Article 13.4.4. MR3056628.
Ramsey Theory on the Integers SAT-Solving Abstract

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003. On computation of exact van der Waerden numbers journal
Tanbir Ahmed, Integers, 12 (3) (2012), 417-425. Online version: 11 (2011), A71. MR2955523.
Ramsey Theory on the Integers SAT-Solving Abstract

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002. Two new van der Waerden numbers: w(2; 3, 17) and w(2; 3, 18) journal
Tanbir Ahmed, Integers, 10 (2010), 369-377, A32. MR2684128.
Ramsey Theory on the Integers SAT-Solving Abstract
-- First applied DIVIDE-AND-CONQUER Distributed SAT-Solving to compute these numbers in around 2009.

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001. Some new van der Waerden numbers and some van der Waerden-type numbers journal
Tanbir Ahmed, Integers, 9 (2009), 65-76, A06 MR2506138.
Ramsey Theory on the Integers SAT-Solving Abstract
--- (See tawSolver 1.0: an efficient implementation of the DPLL Algorithm.)

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