PUBLICATIONS

Research Publications

Student coauthors are listed in purple.

Under Review

46.    Parking functions: Choose your own adventure

with Joshua Carlson, Alex Christensen, Zakiya Jones, and Andres Ramos Rodriguez. Submitted.

45.    A generalization of parking functions with backward movement

with Alex Christensen, Zakiya Jones, Marissa Loving, Andres Ramos Rodriguez, Joseph Rennie, and Gordon Rojas Kirby. Submitted.

44.    On (t,r) broadcast domination of certain grid graphs

with Natasha Crepeau, Sean Hays, Marissa Loving, Joseph Rennie, Gordon Rojas Kirby, and Alexandro Vasquez. Submitted.

43.    Visualizing the support of Kostant's weight multiplicity formula for the rank two Lie algebras

with Marissa Loving, Juan Ramirez, Joseph Rennie, Gordon Rojas Kirby, Eduardo Torres Davila, and Fabrice O. Ulysse. Submitted.    

 

42.    Generalized lattice point visibility in N^k

with Carolina Benedetti and Santiago Estupinan. Submitted.

 

41.    On lattice point weak b-visibility

with Allie Aird, Alberto Alonso, Samuel I. Cooper, Patrick M. Crossley, Reuben Kaufman, George Kuliner, Robert J. Marino, Eric S. Piato, and Barbara J. Schweitzer. Submitted.   

40.    Phylogenetic trees

with Hector Banos, Nathaniel Bushek, Ruth Davidson, Elizabeth Gross, Robert Krone, Colby Long, Allen Stewart, and Robert Walker. Submitted.

Accepted / In press

39.    Efficient (t,r) Broadcast Dominating Sets of the Triangular Lattice

with Dalia LuqueClaudia Reyes, and Nohemi Sepulveda. To appear in Discrete Applied Mathematics.

38.    Projects in (t,r) broadcast domination

with Erik Insko and Katie Johnson. To appear in Birkhauser’s Foundations in Undergraduate Research in Mathematics.

37.    Characterizing graphs of critical pairs of layered generalized crowns         

with Rebecca Garcia, Bethany Kubik, and Shannon Talbott. To appear in AKCE International Journal of Graphs and Combinatorics.    

Published
 

36.   Kostant’s Weight Multiplicity Formula and the Fibonacci and Lucas Numbers

with Kevin Chang and Erik Insko.  Journal of Combinatorics, Volume 11, Number 1, 141–167, 2020.

35.    When is the q-multiplicity of a weight equal to a power of q?

with Margaret Rahmoeller, Lisa Schneider, and Anthony Simpson. Electronic Journal of Combinatorics 26(4) (2019), #P4.17.

34.    Generalizations of the feline and Texas chainsaw Josephus problems

with David Ariyibi and Kevin Chang. Open Journal of Discrete Mathematics, Vol. 9 No. 4, Oct 2019.

33.    Counting peaks on graphs

with Alexander Diaz-Lopez, Lucas Everham, Erik Insko, Vincent Marcantonio, and Mohamed Omar. Australasian Journal of Combinatorics Volume 75(2) (2019), Pages 174-189.

32.    Diversity of Artists in Major U.S. Museums

with Chad Topaz, Bernhard Klingenberg, Daniel Turek, Brianna Heggeseth, Julie C. Blackwood, C. Ondine Chavoya, Steven Nelson, Kevin M. Murphy. PLOS One 14 (3) (2019) e0212852.

31.    Block circulant graphs and the graphs of critical pairs of crowns

with Rebecca Garcia, Bethany Kubik, Joseph Pedersen, and Shannon Talbott.  Electronic Journal of Graph Theory and Applications 7  (2) (2019), 207–216.

30.    The graph of critical pairs of a crown

with Fidel Barrera-Cruz, Rebecca E. Garcia, Bethany Kubik, Heather Smith, Shannon Talbott, Elizabeth Taylor, and William T. Trotter. Order (2019) pp. 1-32.

29.    On the genus of a quotient of a numerical semigroup

with Ayomikun Adeniran, Steve Butler, Colin Defant, Yibo Gao, Cyrus Hettle, Qingzhong Liang, Hayan Nam, and Adam Volk. Semigroup Forum (2019), Jan. 3.

28.    Descent polynomials

with Alexander Diaz-Lopez, Erik Insko, Mohamed Omar, and Bruce Sagan. Discrete Mathematics 342 (2019) 1674–1686.

27.   A combinatorial model for computing volumes of flow polytopes

with Carolina Benedetti, Rafael Gonzalez D’Leon, Christopher R. H. Hanusa, Apoorva Khare,

Alejandro Morales and Martha Yip. Transactions of The American Mathematical SocietyVolume 372, Number 5, 1 September 2019, Pages 3369-3404.

26.   Lattice point visibility on power functions

with Mohamed Omar. INTEGERS, Volume 18 (2018) A90.

25.   Optimal (t,r)-broadcast domination on the infinite grid

with Benjamin F. Drews and Timothy W. Randolph. Discrete Applied Mathematics, Volume 255, 28 February 2019, Pages 183-197.

24.    Bin Decompositions

with Daniel Gotshall, Dawn Nelson, Maria Vega, and Cameron Voigt. Involve, a Journal of Mathematics, 2019, vol. 12, no. 3, pp. 503--519.

23.    Dimensions of group-based phylogenetic mixtures

with Hector Banos, Nathaniel Bushek, Ruth Davidson, Elizabeth Gross, Robert Krone, Colby Long, Allen Stewart, and Robert Walker. Bulletin of Mathematical Biology (2019) 81:316–336.


22.    The volume of the caracol polytope

with Carolina Benedetti, Rafael Gonzalez D'Leon, Christopher R. H. Hanusa, Apoorva Khare, Alejandro Morales and Martha Yip. Seminaire Lotharingien de Combinatoire XX (2018) Proceedings of the 30th Conference on Formal Power Series, Article #YY, 12 pp. Series and Algebraic Combinatorics (Hanover).
 

21.    Sequences of consecutive happy numbers in negative bases

with Helen G. Grundman. The Fibonacci Quarterly, Volume 56, Number 3, August 2018, p. 221-228.

20.    Lattice patterns for the support of Kostant’s weight multiplicity formula on sl_3(C)

with Haley Lescinsky, Grace Mabie. Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 4, n. 1, June 2018.

19.    Lattice point visibility on generalized lines of sight

with Edray Goins, Bethany Kubik, and Aba Mbirika. The American Mathematical Monthly (2018), 125:7, 593-601.

18.    The q-analog of Kostant’s partition function and the highest root of the simple Lie algebras

with Erik Insko, and Mohamed Omar. Australasian Journal of Combinatorics Volume 71(1) (2018) 68–91.

17.    A minimaj-preserving crystal on ordered multiset partitions

with Georgia Benkart, Laura Colmenarejo, Rosa Orellana, Greta Panova, Anne Schilling, and Martha Yip. Advances in Applied Mathematics 95 (2018) 96–115.

16.    Computing weight q-multiplicities for the representations of the simple Lie algebras

with Erik Insko, and Anthony Simpson. Applicable Algebra in Engineering, Communication and Computing, 29(4), August 2018, Volume 29, Issue 4, pp 351-362.

15.    Computing weight multiplicities

In: Wootton A., Peterson V., Lee C. (eds) A Primer for Undergraduate Research. Foundations for Undergraduate Research in Mathematics. Birkhauser, Cham (2017) 193-222.

14.    New Behavior in Legal Decompositions Arising from Non-positive Linear Recurrences

with Minerva Catral, Pari Ford, Steven J. Miller, Dawn Nelson, Zhao Pan, and Huanzhong Xu. The Fibonacci Quarterly 55 (2017), no. 3, 252–275.

13.    Weight q-multiplicities for representations of sp4(C)

with Edward L. Lauber. Journal of Siberian Federal University. Mathematics & Physics 2017, 10(4), 1-9.

12.    A proof of the peak polynomial positivity conjecture

with Alexander Diaz-Lopez, Erik Insko, and Mohamed Omar. Seminaire Lotharingien de Combinatoire 78B (2017) Article #6, 9 pp. Proceedings of the 29th Conference on Formal Power Series and Algebraic Combinatorics (London).

11.    A proof of the peak polynomial positivity conjecture

with Alexander Diaz-Lopez, Erik Insko, and Mohamed Omar. Journal of Combinatorial Theory, Series A 149 (2017) 21–29.

10.    A Note on Monovariants and Minimal Fibonacci Representations

with Minerva Catral, Pari Ford, Steven Miller, and Dawn Nelson, Featured Article in the Metro Math Newsletter, Metropolitan New York Section of the Mathematical Association of America, April 2017.

9.      Peak Sets of Classical Coxeter Groups

with Alexander Diaz-Lopez, Erik Insko, and Darleen Perez-Lavin. Involve, a Journal of Mathematics, 2017, vol. 10, no. 2, pp. 263–290.

8.      Individual Gap Measures from Generalized Zeckendorf Decompositions

with Robert Dorward, Pari Ford, Eva Fourakis, Steven J. Miller, Eyvi Palsson, and Hannah Paugh. Uniform Distribution Theory 12 (2017), no. 1, 27–36.     

                    

7.      A Generalization of Zeckendorf’s Theorem via Circumscribed m-gons

with Robert Dorward, Pari Ford, Eva Fourakis, Steven J. Miller, Eyvi Palsson, and Hannah Paugh. Involve, a Journal of Mathematics 10-1 (2017), 125–150.

6.      Legal Decompositions Arising from Non-positive Linear Recurrences

with Minerva Catral, Pari Ford, Steven J. Miller, and Dawn Nelson. The Fibonacci Quarterly 54 (2016), no. 4, 348–365. 

5.      The adjoint representation of a classical Lie algebra and the support of Kostant’s weightmultiplicity formula

with Erik Insko, and Lauren Kelly Williams. Journal of Combinatorics Volume 7 (2016) Number 1 pp. 75-116.

4.      Generalizing Zeckendorf’s Theorem: The Kentucky Sequence

with Minerva Catral, Pari Ford, Steven J. Miller, Dawn Nelson. Fibonacci Quarterly 52 (2014), no. 5, 68–90.

3.      Sums of squares of Littlewood-Richardson coefficients and GLn-harmonic polynomials

with Jeb F. Willenbring. Symmetry: Representation Theory and its Applications Ed. Hunziker, Markus and Howe, Roger. Springer (2014).

2.      Combinatorial problems related to Kostant’s weight multiplicity formula

Ph.D. Thesis, Advisor: Jeb Willenbring. University of Wisconsin Milwaukee 2012.

1.      On the adjoint representation of sl_n and the Fibonacci numbers

C. R. Math. Acad. Sci. Paris 349 (2011) pp. 935-937. 

 


Pedagogy Publications 

3.      Contagious: A Network Science Approach to Defending Your Digital World 

with Bethany Kubik, Alicia Prieto-Langarica, and Debra Mimbs. Command, Control, and Interoperability Center for Advanced Data Analysis (CICCADA) a Department of Homeland Security Center of Excellence, Module for Undergraduate Students, 2015. This includes the student and faculty version.

2.      Success Indicators in the USMA Advanced Core Mathematics Program 

with James Starling, Jarrod Shingleton, and Christopher Thoma. Proceedings of the 2015 Joint Statistical Meetings, CDAS, 2014, pp. 4055-4066.

1.      Strengthening Communication Skills through Cadet Created Homework Videos 

Mathematica Militaris, Volume 21, Issue 2, Spring 2013, pp. 3-18. 

Writing Contributions to the Profession

24.    Importance of the Latinx Mathematical Community

with Erika Camacho and Bill Velez. Revising.

23.    When Undergraduate Research Work, Works!

with Alex Christensen, Zakiya Jones, Juan Ramirez, and Fabrice O. Ulysse. Submitted.

22.    Ban on Hotel Room Interviews

with Susan Crook, Alicia Prieto Langarica, and Lola Thompson. Submitted.

21.    The Undergraduate Mathematics Classroom as a Publishing House: A New Type of Learning Community

Submitted. 

20.    Avoiding toxic mentoring

e-Mentoring Network in the Mathematical Sciences - connecting students and mentors. AMS blogs. September 27, 2019.

19.    It's the little things

e-Mentoring Network in the Mathematical Sciences - connecting students and mentors. AMS blogs. August 28, 2019.

18.    Co-mentoring collaborations

with Alicia Prieto Langarica. MAA FOCUS, August/September 2019 p. 18-19.

17.    2019 Lathisms: Latinxs and Hispanics in the Mathematical Sciences

with Alicia Prieto Langarica and Luis Sordo Vieira. To appear in Notices of the American Mathematical Society.

16.    Lathisms

with Guadalupe Lozano, Alicia Prieto Langarica, and Luis Sordo Vieira. MAA FOCUS, June/July 2019, p. 22-24.

15.    Manuscript Pre-Submission Check List

e-Mentoring Network in the Mathematical Sciences - connecting students and mentors. AMS blogs. March 26, 2019.

14.    A Mathematical Journey of Culture, Community, and Collaboration

Notices of the American Mathematical Society, Volume 66, Number 1, p. 94.

13.     The Harrasment is Real 

p. 71-72 in book ``Living Proof: Stories of Resilience Along the Mathematical Journey,'' Editors: Allison K. Henrich, Emille D. Lawrence, Matthew A. Pons, and David G. Taylor. AMS/MAA Publication, 2019. 

12.    2018 Lathisms: Latinxs and Hispanics in the Mathematical Sciences

with Alexander Diaz-Lopez, Alicia Prieto Langarica, Gabriel Sosa. September 2018, Notices of the American Mathematical Society, Volume 65, Number 8.

11.    Math Mamas: Changing the Narrative

with Becky Hall, Emille Lawrence, and Carrie Diaz Eaton, Journal of Humanistic Mathematics, Volume 8 Issue 2 (July 2018), pages 2-4.
 

10.    Partitions from Mars, Part 2

with Alex Pankhurst, Cielo Perez and Aesha Siddiqui. Girls’ Angle Bulletin, February/March 2018 Volume 11 Number 3 p. 7-10.

9.      Partitions from Mars, Part 1

with Alex Pankhurst, Cielo Perez and Aesha Siddiqui. Girls’ Angle Bulletin, December 2017/January 2018 Volume 11 Number 2 p. 7-11.

8.      Advising Underrepresented Minorities in Mathematics Research

with Cynthia Flores, Alicia Prieto Langarica, and Shelby Wilson. To appear as a passage in book for faculty on how to successfully mentor undergraduate students in research authored by Michael Dorff, Allison Henrich, and Lara Pudwell.

7.      Mathematics and Motherhood

with Carrie Diaz Eaton, Becky Hall, and Emille Davie Lawrence. The National Association of Mathematicians Newsletter Volume XLVIII, Number 2, Summer 2017.

6.      Searching for a sense of belonging 

with Alicia Prieto-Langarica. Stories from the Front of the Room: How Higher Education Faculty of Color Overcome and Thrive in the Academy, Rowman & Littlefield 2017.

5.      Actively Embracing Mentoring

e-Mentoring Network in the Mathematical Sciences - connecting students and mentors. AMS blogs. January 26, 2017.

4.      Exploring Undergraduate Research with Diverse Mathematicians at MAA MathFest 

with Alicia Prieto Langarica. The National Association of Mathematicians Newsletter Volume XLVII, Number 3, Fall 2016.

3.      Lathisms: Latinos and Hispanics in the Mathematical Sciences 

with Alexander Diaz-Lopez, Alicia Prieto Langarica, Gabriel Sosa. October 2016 issue of The Notices of the AMS.

2.      New year, same goal: more research

e-Mentoring Network in the Mathematical Sciences - connecting students and mentors. AMS blogs. March 1, 2016.​

1.      Building a Research Army

e-Mentoring Network in the Mathematical Sciences - connecting students and mentors. AMS blogs. October 15, 2015. 

Williams College

Department of Mathematics and Statistics

33 Stetson Ct Office 106C

Williamstown MA 01267