Publications

Accepted

• R. Garcia, P. Harris, M. Loving, L. Martinez, D. Melendez, J. Rennie, G. Rojas Kirby, and D. Tinoco, "On Kostant's weight q-multiplicity formula for sl_4(C)," Accepted July 2020 in Applicable Algebra in Engineering, Communications, and Computing. (Received award for 2022 Best Paper in AAECC!!)

• S. Chapman, R. Garcia, C. O'Neill, "Beyond Coins, Stamps, and Chicken McNuggets: an Invitation to Numerical Semigroups," Accepted November 2019, a Chapter included in Springer series Foundations for Undergraduate Research in Mathematics.

Published

• F. Barrera-Cruz, R. Garcia, P. Harris, B. Kubik, H. Smith, S. Talbott, L. Taylor, and W. T. Trotter, "The Graph of Critical Pairs of a Crown," Order 36, 621 - 652 (2019).

• R. Garcia, P. Harris, B. Kubik, S. Talbott, "Characterizing graphs of critical pairs of layered generalized crowns," AKCE International Journal of Graphs and Combinatorics, 17:1, 387-401, DOI: 10.1016/j.akcej.2019.03.001

• R. Garcia, P. Harris, B. Kubik, S. Talbott, "Block Circulant and the Graphs of Critical Pairs of a Crown." Electronic Journal of Graph Theory and Applications 7 (2), 207 - 216 (2019)

• E. Petersen, N. Youngs, R. Kruse, D. Miyata, R. Garcia, L. D. García Puente (2018) "Neural Ideals in SageMath." In: Davenport J., Kauers M., Labahn G., Urban J. (eds) Mathematical Software -- ICMS 2018. ICMS 2018. Lecture Notes in Computer Science, Vol.~10931. Springer, Cham. https://doi.org10.1007/978-3-319-96418-8_22, arXiv: 1609.09602

• L. García Puente, R. Garcia, J. Liu, R. Kruse, D. Miyata, E. Peterson, K. Phillipson, A. Shiu, "Gröbner Bases of Neural Ideals.''  International Journal of Algebra and Computation. Vol. 28, No. 04, pp. 553--571 (2018), arXiv: 1612.05660

• R. Garcia and D. Silva, "Order Dimension of Layered Generalized Crowns,'' Ars Combinatoria, Vol. CXIIIA, January 2014, p. 171 - 186

• S. Chapman, L. García Puente, R. Garcia, M. Malandro, and K. Smith, "Algebraic and combinatorial aspects of sandpile monoids on directed graphs,'' Journal of Combinatorial Theory, Series A, 120 (2013) 245 - 265

• R. Garcia, C. Wyels, "Broadening Participation and Promoting Success,'' Involve Special Issue: Trends in Undergraduate Research in the Mathematical Sciences (Chicago, 2012), Vol. 7, No. 3, (2014) p. 315 - 326. DOI: 10.2140/involve.2014.7-3

• R. Garcia, M. Lane and B. Loft, "Enumeration and Construction of Magic n Circles,'' Mathematics and Computers in Simulation, 82 (2011) 44 - 53

• R. Garcia, S. Meyer, S. Sanders, and A. Seitz, "Construction and enumeration of Franklin circles,'' Involve 2, Issue 3 (2009), 357 - 370

• R. Garcia, "On the Minors of Catalecticant Matrices and on the Coadunation of Generalized Crowns,'' Ph.D. Dissertation, New Mexico State University (2004)

• R. Garcia (as R. Pablo), J. Little, D. Ortiz, R. Ortiz-Rosado, and K. Rios-Soto, "Some Remarks on Fitzpatrick and Flynn's Gröbner Basis Technique for Padé Approximation,'' Journal of Symbolic Computation  35 (2003), 451-461

Collaborators