References
- [Billey et al. 93] S. C. Billey, W. Jockusch, and R. P. Stanley. “Some Combinatorial Properties of Schubert Polynomials.” J. Algebr. Combin. 2 (1993), 345–374.
- [Blake and Huffman 13] I. Blake and W. C. Huffman. “Basic Coding Properties and Bounds.” In Handbook of Finite Fields, edited by G. L. Mullen and D. Panario, pp. 659–703. Boca Raton, FL: Chapman & Hall/CRC, 2013.
- [Delsarte 78] P. Delsarte. “Bilinear Forms Over a Finite Field, with Applications to Coding Theory.” J. Combin. Theory Ser. A 25: 3 (1978), 226–241.
- [Dworkin 98] M. Dworkin. “An Interpretation for Garsia and Remmel’s q-Hit Numbers.” J. Combin. Theory Ser. A 81: 2 (1998), 149–175.
- [Garsia and Remmel 86] A. M. Garsia and J. B. Remmel. “Q-Counting Rook Configurations and a Formula of Frobenius.” J. Combin. Theory Ser. A 41: 2 (1986), 246–275.
- [Gasper and Rahman 04] G. Gasper and M. Rahman. Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications), vol. 96, second edition. Cambridge: Cambridge University Press, 2004. With a foreword by Richard Askey.
- [Goldman et al. 75] J. R. Goldman, J. T. Joichi, and D. E. White. “Rook Theory. I. Rook Equivalence of Ferrers Boards.” Proc. Amer. Math. Soc. 52 (1975), 485–492.
- [Haglund 98] J. Haglund. “q-Rook Polynomials and Matrices Over Finite Fields.” Adv. Appl. Math. 20: 4 (1998), 450–487.
- [Kaplan et al. 18] N. Kaplan, J. B. Lewis, and A. H. Morales. Work in progress, 2018+.
- [Kaplansky and Riordan 46] I. Kaplansky and J. Riordan. “The Problem of the Rooks and its Applications.” Duke Math. J. 13 (1946), 259–268.
- [Klein et al. 14] A. J. Klein, J. B. Lewis, and A. H. Morales. “Counting Matrices Over Finite Fields with support on Skew Young Diagrams and Complements of Rothe Diagrams.” J. Algebraic Combin. 39: 2 (2014), 429–456.
- [Lewis et al. 11] J. B. Lewis, R. I. Liu, A. H. Morales, G. Panova, S. V. Sam, and Y. X. Zhang. “Matrices with Restricted Entries and q-Analogues of Permutations.” J. Comb. 2: 3 (2011), 355–395.
- [Lewis and Morales 16] J. B. Lewis and A. H. Morales. “Combinatorics of Diagrams of Permutations.” J. Combin. Theory Ser. A 137 (2016), 273–306.
- [Lewis and Morales 17] J. B. Lewis and A. H. Morales. “Counting Matrices Over Finite Fields: Code and Data.” Available online https://sites.google.com/site/matrixfinitefields/, 2017.
- [MacWilliams 63] J. MacWilliams. “A Theorem on the Distribution of Weights in a Systematic Code.” Bell System Tech. J. 42 (1963), 79–94.
- [Manivel 01] L. Manivel. Symmetric Functions, Schubert Polynomials and Degeneracy Loci (SMF/AMS Texts and Monographs), vol. 6. Providence, RI; Paris: American Mathematical Society; Société Mathématique de France, 2001.
- [Morrison 06] K. E. Morrison. “Integer Sequences and Matrices Over Finite Fields.” J. Integer Seq. 9:2 (2006), Article 06.2.1.
- [Ravagnani 17] A. Ravagnani. “Duality of Codes Supported on Regular Lattices, with an Application to Enumerative Combinatorics.” Des. Codes Cryptogr. 2017. https://doi.org/10.1007/s10623-017-0436-3.
- [Stanley 12] R. P. Stanley. Enumerative Combinatorics. Volume 1 (Cambridge Studies in Advanced Mathematics), vol. 49, second edition. Cambridge: Cambridge University Press, 2012.
- [Stanton 84] D. Stanton. “Orthogonal Polynomials and Chevalley Groups.” In Special Functions: Group Theoretical Aspects and Applications, edited by R. A. Askey, T. H. Koornwinder and W. Schempp, pp. 87–128, Math. Appl. Dordrecht: Reidel, 1984.
- [Stembridge 98] J. R. Stembridge. “Counting Points on Varieties Over Finite Fields Related to a Conjecture of Kontsevich.” Ann. Comb. 2: 4 (1998), 365–385.
- [Stembridge 09] J. R. Stembridge. “The Kontsevich Conjecture.” Available at http://www.math.lsa.umich.edu/jrs/archive.html, 2009.
- [The Sage Developers 17] The Sage Developers. SageMath, the Sage Mathematics Software System (Version 7.6), 2017. Available at http://www.sagemath.org.
- [Valiant 79] L. G. Valiant. “The Complexity of Computing the Permanent.” Theoret. Comput. Sci. 8: 2 (1979), 189–201.