Nathan McNew
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  1. Efficient realization of nonzero spectra by polynomial matrices (Undergraduate Thesis, 2010)
    N. McNew and N. Ormes, Involve, 8 (2015), 1-24.

  2. Radically weakening the Lehmer and Carmichael conditions
    N. McNew, International Journal of Number Theory, 9 (2013), 1215-1224.

  3. On sets of integers which contain no three terms in geometric progression
    N. McNew, Mathematics of Computation, 84 (2015), 2893-2910.

  4. Geometric-progression-free sets over quadratic number fields (SMALL REU 2014)
    A. Best, K. Huan, N. McNew, S. Miller, J. Powell, K. Tor, and M. Weinstein, The Royal Society of Edinburgh Proceedings A, 147 (2017), 245-262.

  5. Popular values of the largest prime divisor function
    N. McNew. Experimental Mathematics, 26 (2017), 210-224.

  6. Ramsey theory problems over the integers: avoiding generalized progressions (SMALL REU 2014)
    A. Best, K. Huan, N. McNew, S. Miller, J. Powell, K. Tor, and M. Weinstein, in Combinatorial and Additive Number Theory II. CANT 2015, CANT 2016. Nathanson, M. (ed) Springer Proceedings in Mathematics & Statistics, 220 (2017). Springer, New York, NY, 39-52.

  7. Infinitude of k-Lehmer numbers which are not Carmichael
    N. McNew and T. Wright, International Journal of Number Theory, 12 (2016), 1863-1869.

  8. Numbers divisible by a large shifted prime and large torsion subgroups of CM elliptic curves
    N. McNew, P. Pollack, and C. Pomerance, Int. Math. Res. Not. IMRN, 18 (2017), 5525-5553.

  9. Subsets of F_q[x] free of 3-term geometric progressions (SMALL REU 2015)
    M. Asada, E. Fourakis, S. Manski, N. McNew, S. Miller and G. Moreland, Finite Fields and Their Applications, 44 (2017), 135-147.

  10. When sets can and cannot have sum-dominant subsets
    H. Chu, N. McNew, S. Miller, Victor Xu and Sean Zhang, Journal of Integer Sequences, 21 (2018) Article 18.8.2.

  11. Random multiplicative walks on the residues modulo n
    N. McNew, Mathematika, 63 (2017), 602-621.

  12. The convex hull of the prime number graph
    N. McNew, in Irregularities in the Distribution of Prime Numbers Pintz J., Rassias M. (eds) Springer, Cham (2018), 125-141.

  13. Avoiding 3-term geometric progressions in non-commutative settings (SMALL REU 2015)
    M. Asada, E. Fourakis, S. Manski, N. McNew, S. Miller and G. Moreland.

  14. Counting Primitive Subsets and other statistics of the divisor graph of {1,2,... n}
    N. McNew, European Journal of Combinatorics. 92 (2021) 103237.

  15. Primitive and geometric-progression-free sets without large gaps
    N. McNew, Acta Arithmetica, 192 (2020), 95-104.

  16. Counting pattern-avoiding integer partitions
    J. Bloom and N. McNew, The Ramanujan Journal, 55 (2021), 555-591.

  17. On the size of primitive sets in function fields (SUMRY 2019)
    A. Gómez-Colunga, C. Kavaler, N. McNew and M. Zhu, Finite Fields and their Applications, 64 (2020), 101658.

  18. On the Erdős primitive set conjecture in function fields (SUMRY 2019, see also the related code.)
    A. Gómez-Colunga, C. Kavaler, N. McNew and M. Zhu. Journal of Number Theory. 219 (2021), 412-444.

  19. Unknotted Cycles
    C. Cornwell and N. McNew. Electronic Journal of Combinatorics. 29 (2022), P3.50.

  20. Note on sets without geometric progressions
    X. Cao, J. Fang and N. McNew. Integers, 22 (2022) #A45.

  21. Permutations and the Divsor Graph of [1,n]
    N. McNew. Mathematika, 69 (2023), 51--67.

  22. Explicit bounds for large gaps between squarefree integers (Towson REU 2022)
    A. Kumchev, W. McCormick, N. McNew, A. Park, R. Scherr and S. Ziehr Journal of Number Theory, 254 (2024), 336--357.

  23. Intermediate prime factors in specified subsets
    N. McNew, P. Pollack, A. Singha Roy. Monatschafte fur Mathematik. 202 (2023), 837--855.

  24. The distribution of intermediate prime factors
    N. McNew, P. Pollack, A. Singha Roy

  25. Links and the Diaconis-Graham inequality
    C. Cornwell and N. McNew, to appear in Combinatorica.

  26. Short Interval Results For Powerfree Polynomials Over Finite Fields (Towson REU 2022)
    A. Kumchev, N. McNew, A. Park, to appear in International Journal of Number Theory.


(Out of date)


  1. The Second Carib War, N. McNew, Rocky Mountain Undergraduate Review 2 (2009)
  2. Research in history done while I was an undergraduate on an island war which played a small role in the greater French Revolution.

  3. Random Walks with Restarts, 3 Examples
  4. A survey article I wrote for a course at Dartmouth which corrects an example given in On Playing Golf With Two Balls by Dumitriu, and Tetali, and Winkler.
    It also presents a new heuristic argument for the asymptotic hitting time with restarts on a 2-D lattice.

    Graph of the Sum of Factors Function

Copyright © 2023 Nathan McNew