Elementary works

Works understandable at an undergraduate level or below (level 3 or lower). Level 3 means advanced undergraduate; level 2 is contest mathematics.

119 records
2026. Darij Grinberg. A determinant identity for symmetric matrices (last updated June 4, 2026).
2026. GPT-5.5, Darij Grinberg. A Universal Noncommutative Splitting Algebra for Polynomials (last updated July 12, 2026).
2026. Darij Grinberg, Benjamin Liber. An equality for balanced digraphs (last updated May 18, 2026). arXiv:2507.22388. The Electronic Journal of Combinatorics, 33, 2026, issue 3, P3.19.
2026. GPT-5.5, Darij Grinberg. Cohn's theorem on the kernel of the Dynkin operator (last updated July 12, 2026).
2026. GPT-5.6 Sol, Darij Grinberg. Collapsibility of Alexander duals for shade maps (last updated August 30, 2026).
2026. Darij Grinberg. Compositions of n-homomorphisms (last updated April 13, 2026). arXiv:2604.13619.
2026. Darij Grinberg, Tom Roby. Detropicalization as a proof technique (last updated May 28, 2026). arXiv:2605.30511.
2026. Darij Grinberg. Elementary derivations of some results of linear optimization (last updated July 8, 2026).
2026. Darij Grinberg, Peter Mao. Necklaces over a group with identity product (last updated August 4, 2026). arXiv:2405.08937. Journal of Integer Sequences 29 (2026), Article 26.4.6.
2026. Darij Grinberg. Noncommutative Abel-like identities (last updated April 14, 2026). arXiv:2604.12619.
2026. Darij Grinberg. Note on the Young–Jucys–Murphy elements (last updated May 29, 2026).
2026. Benjamin Adenbaum, Darij Grinberg. On the q-Poincaré sum of a Coxeter group (last updated July 11, 2026).
2026. GPT-5.6 Sol, Darij Grinberg. Polynomials over Symmetric Polynomials (last updated August 9, 2026).
2026. Darij Grinberg, Hamesh M. Hamesh. Powers of matrices with all principal minors equal to 1 (last updated August 1, 2026). arXiv:2606.28976.
2026. GPT-5.5, Darij Grinberg. Splitting a Polynomial into Linear Factors after an Injective Ring Extension (last updated July 19, 2026).
2026. Darij Grinberg. The V/L recursion for Macdonald's 7th Variation Schur polynomials (last updated June 1, 2026). arXiv:2605.26775.
2025. Darij Grinberg. An Introduction to Algebraic Combinatorics (last updated July 22, 2026). arXiv:2506.00738.
2025. Darij Grinberg. An introduction to the algebra of rings and fields (last updated September 12, 2026). arXiv:2508.13165.
2025. Darij Grinberg. An introduction to the symmetric group algebra (last updated July 4, 2026). arXiv:2507.20706.
2025. Darij Grinberg. Discrete Mathematics (last updated May 16, 2026).
2025. Darij Grinberg. Rook sums in the symmetric group algebra (last updated July 11, 2026). arXiv:2507.22386.
2025. Darij Grinberg. The trace Cayley-Hamilton theorem (last updated June 17, 2026). arXiv:2510.20689.
2024. Darij Grinberg. Mathematical Problem Solving (last updated August 11, 2026).
2024. Darij Grinberg, Tom Roby, Stephan Wagner, Mei Yin. Monomial identities in the Weyl algebra (last updated May 5, 2026). arXiv:2405.20492.
2024. Darij Grinberg, Nazar Korniichuk, Kostiantyn Molokanov, Severyn Khomych. The diagonal derivative of a skew Schur polynomial (last updated June 6, 2026). arXiv:2402.14217.
2024. Morten Brun, Darij Grinberg. The Dowker theorem via discrete Morse theory (last updated July 22, 2024). arXiv:2407.15454.
2024. Darij Grinberg. The entry sum of the inverse Cauchy matrix (last updated June 6, 2026). arXiv:2301.09777. The Mathematical Intelligencer 46 (2024), no. 1, pp. 46--48.
2023. Darij Grinberg, Tom Roby. Birational rowmotion on a rectangle over a noncommutative ring (last updated June 17, 2026). arXiv:2208.11156. Combinatorial Theory 3, 2023, no. 7.
2023. Darij Grinberg. Graph Theory (last updated September 10, 2026). arXiv:2308.04512.
2023. Jonah Blasiak, Omesh Dhar Dwivedi, Darij Grinberg. Multislant matrices and Jacobi--Trudi determinants over finite fields (last updated June 7, 2023). arXiv:2302.07239. Finite Fields and Their Applications 91, 2023, 102262.
2023. Darij Grinberg, Nazar Korniichuk, Kostiantyn Molokanov, Severyn Khomych. The Pak–Postnikov and Naruse skew hook length formulas: a new proof (last updated May 19, 2026). arXiv:2310.18275.
2023. Darij Grinberg, Richard P. Stanley. The Redei--Berge symmetric function of a directed graph (last updated June 13, 2026). arXiv:2307.05569.
2022. Darij Grinberg. Elemente der Mathematik Problem 1414: gcds of recursively defined sequences (with solution) (last updated July 14, 2022). Elemente der Mathematik 77 (2022), pp. 146--152.
2022. Darij Grinberg. On the principal minors of the powers of a matrix (last updated July 3, 2026). arXiv:2204.07885. Gazeta Matematica 2022, issue 1-2, pp. 1--13.
2022. Omesh Dhar Dwivedi, Darij Grinberg. On the rank of Hankel matrices over finite fields (last updated June 6, 2026). arXiv:2109.05415. Linear Algebra and its Applications 641, 15 May 2022, pp. 156--181.
2022. Darij Grinberg. Petrie symmetric functions (last updated June 15, 2026). arXiv:2004.11194. Algebraic Combinatorics 5 (2022), no. 5, pp. 947--1013.
2022. Darij Grinberg, Zhi-Wei Sun, Lilu Zhao. Proof of three conjectures on determinants related to quadratic residues (last updated November 16, 2020). arXiv:2007.06453. Linear and Multilinear Algebra 70 (2022), no. 19, pp. 3734--3746.
2022. Darij Grinberg. Similar matrices and equivalent polynomial matrices (last updated June 13, 2026).
2022. Darij Grinberg, Nadia Lafrenière. The one-sided cycle shuffles in the symmetric group algebra (last updated June 12, 2026). arXiv:2212.06274. Algebraic Combinatorics 7 (2024), no. 2, pp. 275--326.
2021. Darij Grinberg. A double Sylvester determinant (last updated June 9, 2026). arXiv:1901.11109. Ars Mathematica Contemporanea 20 (2021), no. 2, pp. 261--274.
2021. Darij Grinberg, Fedor Petrov. A greedoid and a matroid inspired by Bhargava's p-orderings (last updated June 13, 2026). arXiv:1909.01965. The Electronic Journal of Combinatorics 28(3) (2021), #P3.6.
2021. Darij Grinberg. Alternierende Summen: Aufgaben und Lösungen (last updated August 7, 2026).
2021. Darij Grinberg. Einführung in algebraische Ungleichungen I (last updated August 6, 2026).
2021. Alberto Dennunzio, Enrico Formenti, Darij Grinberg, Luciano Margara. Integrality of matrices, finiteness of matrix semigroups, and dynamics of linear cellular automata (last updated June 16, 2026). arXiv:1907.08565. Parts of this preprint have been incorporated into An efficiently computable characterization of stability and instability for linear cellular automata, Journal of Computer and System Sciences 122 (2021), pp. 63--71.
2021. Darij Grinberg. Introduction to Modern Algebra (last updated April 19, 2026).
2021. Darij Grinberg. The Elser nuclei sum revisited (last updated August 6, 2026). arXiv:2009.11527. Discrete Mathematics & Theoretical Computer Science 23 (2021), no. 1, article 7012.
2021. Darij Grinberg, Lukas Katthän, Joel Brewster Lewis. The path-missing and path-free complexes of a directed graph (last updated June 21, 2026). arXiv:2102.07894.
2021. Darij Grinberg. The pre-Pieri rules (last updated May 21, 2026). arXiv:2110.03108.
2020. Darij Grinberg, Jia Huang, Victor Reiner. Critical groups for Hopf algebra modules (last updated June 13, 2026). arXiv:1704.03778. Mathematical Proceedings of the Cambridge Philosophical Society 168 (2020), no. 3, pp. 473--503.
2020. Darij Grinberg. Enumerative Combinatorics (last updated April 26, 2026).
2020. Darij Grinberg. Notes on the combinatorial fundamentals of algebra (last updated July 1, 2026). arXiv:2008.09862.
2020. Darij Grinberg. The Bhargava greedoid as a Gaussian elimination greedoid (last updated June 19, 2026). arXiv:2001.05535. The Electronic Journal of Combinatorics 31(2) (2024), #P2.28.
2020. Darij Grinberg. Why Ring(A, k) / G injects into Ring(AG, k) (last updated April 24, 2026).
2019. Darij Grinberg. An exercise on determinant-like sums (last updated May 21, 2026).
2019. Darij Grinberg. Commutators, matrices and an identity of Copeland (last updated June 17, 2026). arXiv:1908.09179.
2019. Darij Grinberg. Integrality over ideal semifiltrations (last updated May 18, 2026). arXiv:1907.06125.
2019. Alberto Dennunzio, Enrico Formenti, Darij Grinberg, Luciano Margara. On coprime characteristic polynomials over finite fields (last updated June 16, 2026). This is a (slightly rewritten) self-contained fragment of the paper Alberto Dennunzio, Enrico Formenti, Darij Grinberg, Luciano Margara, Chaos and ergodicity are decidable for linear cellular automata over (Z/mZ)n, Information Sciences 539 (2020), pp. 136--144..
2019. Darij Grinberg. Regular elements of a ring, monic polynomials and "lcm-coprimality" (last updated May 21, 2026).
2019. Darij Grinberg, Peter Olver. The n body matrix and its determinant (last updated March 2, 2019). arXiv:1802.02900. SIAM Journal on Applied Algebra and Geometry 3(1), 2019, pp. 67--86.
2018. Darij Grinberg. Notes on network flows (last updated November 16, 2018).
2018. Darij Grinberg. The 4-periodic spiral determinant (last updated June 5, 2026).
2018. Darij Grinberg. The Lucas and Babbage congruences (last updated June 28, 2026).
2017. Darij Grinberg. Double posets and the antipode of QSym (last updated June 21, 2026). arXiv:1509.08355. The Electronic Journal of Combinatorics 24, Issue 2 (2017), Paper #P2.22.
2017. Darij Grinberg. On binomial coefficients modulo squares of primes (last updated June 28, 2026). arXiv:1712.02095. Integers: Electronic Journal of Combinatorial Number Theory 19 (2019), A14.
2017. Darij Grinberg. Why the log and exp series are mutually inverse (last updated December 15, 2017).
2016. Darij Grinberg. 18.781 (Spring 2016): Floor and arithmetic functions (last updated June 5, 2026).
2016. Darij Grinberg, Karthik Karnik, Anya Zhang. A generalization of Chio Pivotal Condensation (last updated May 7, 2026). arXiv:1606.08193.
2016. Darij Grinberg. A note on bilinear forms (last updated June 13, 2026).
2016. Darij Grinberg. Fleck's binomial congruence using circulant matrices (last updated June 12, 2026).
2016. Darij Grinberg. Generalized Whitney formulas for broken circuits in ambigraphs and matroids (last updated June 15, 2026). arXiv:1604.03063.
2016. Darij Grinberg, Tom Roby. Iterative properties of birational rowmotion (last updated May 3, 2026). arXiv:1402.6178. (part 1) Electronic Journal of Combinatorics 23 (2016), Paper #P1.33; (part 2) Electronic Journal of Combinatorics 22 (2015), Paper #P3.40.
2016. Darij Grinberg. Notes on linear algebra (last updated April 22, 2026).
2016. Darij Grinberg. On p-polynomials and Fp-vector subspaces of fields (last updated June 15, 2026).
2016. Pavel Galashin, Darij Grinberg, Gaku Liu. Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions (last updated May 5, 2026). arXiv:1509.03803. The Electronic Journal of Combinatorics 23, Issue 3 (2016), Paper #P3.14.
2016. Darij Grinberg. Why quaternion algebras have rank 4 (last updated May 21, 2026).
2016. Darij Grinberg. λ-rings: Definitions and basic properties (last updated July 16, 2026).
2015. Darij Grinberg. A constructive proof of Orzech's theorem (last updated April 16, 2026). arXiv:2604.13911.
2015. Darij Grinberg. Collected trivialities on algebra derivations (last updated May 22, 2026).
2015. Victor Kac, Darij Grinberg. Fundamentals of formal distributions (Lecture 3 of Vertex algebras by Victor Kac) (last updated May 4, 2026).
2015. Darij Grinberg. On the PBW theorem for pre-Lie algebras (last updated June 18, 2026).
2015. Darij Grinberg. PRIMES 2015 reading project: Problem set #3 (last updated May 15, 2019).
2014. Darij Grinberg, Victor Reiner. Hopf Algebras in Combinatorics (last updated September 6, 2026). arXiv:1409.8356.
2013. Pavel Etingof, Darij Grinberg. 18.747: Infinite-dimensional Lie algebras (Pavel Etingof, Spring 2012 at MIT) (last updated August 8, 2026).
2013. Darij Grinberg. A note on lifting isomorphisms of modules over PIDs (last updated June 15, 2026).
2013. Darij Grinberg. Mathematical Reflections problem U275 (last updated June 4, 2026).
2013. Darij Grinberg. Witt#5f: Ghost-Witt integrality for binomial rings (last updated April 9, 2017).
2012. Darij Grinberg. A few classical results on tensor, symmetric and exterior powers (last updated June 18, 2026).
2012. Darij Grinberg. A problem on bilinear maps (problem U228 in Mathematical Reflections) (last updated June 4, 2026).
2012. Darij Grinberg. A problem on maxima and rearrangements (Mathematical Reflections Problem O222) (last updated April 29, 2026).
2012. Darij Grinberg. The Clifford algebra and the Chevalley map - a computational approach (last updated July 1, 2026).
2011. Hans-Jürgen Schneider, Darij Grinberg. Hopfalgebren (last updated September 14, 2026).
2011. Darij Grinberg. Poincaré-Birkhoff-Witt type results for inclusions of Lie algebras (last updated July 21, 2026).
2011. Darij Grinberg. Remarks on Krivine's "Lambda-calculus, types and models", Chapter 1, §2 (last updated June 5, 2011).
2011. Darij Grinberg. Two problems on complex cosines (last updated March 18, 2011).
2011. Darij Grinberg. Zeckendorf family identities generalized (last updated April 13, 2026). arXiv:1103.4507.
2010. Darij Grinberg. A hyperfactorial divisibility (last updated June 5, 2026).
2010. Darij Grinberg. Rep#1: Deformations of a bimodule algebra (last updated June 3, 2026).
2010. Darij Grinberg. Rep#2: An algebraic proof of an analytic lemma (last updated June 4, 2026).
2010. Darij Grinberg. Rep#2a: Finite subgroups of multiplicative groups of fields (last updated June 3, 2026).
2010. Darij Grinberg. Witt#0: Teichmüller representatives (last updated September 5, 2026).
2010. Darij Grinberg. Witt#1: The Burnside Theorem (last updated September 5, 2026).
2010. Darij Grinberg. Witt#2: Polynomials that can be written as wn (last updated September 5, 2026).
2010. Darij Grinberg. Witt#3: Ghost component computations (last updated September 5, 2026).
2010. Darij Grinberg. Witt#4: Some computations with symmetric functions (last updated September 5, 2026).
2010. Darij Grinberg. Witt#4a: Equigraded power series (last updated September 12, 2026).
2010. Darij Grinberg. Witt#4b: A combinatorial identity proven using symmetric functions identities (last updated September 12, 2026).
2010. Darij Grinberg. Witt#5: Around the integrality criterion 9.93 (last updated September 12, 2026).
2010. Darij Grinberg. Witt#5a: Polynomials that can be written as big wn (last updated September 12, 2026).
2010. Darij Grinberg. Witt#5b: Some divisibilities for big Witt polynomials (last updated September 12, 2026).
2010. Darij Grinberg. Witt#5c: The Chinese Remainder Theorem for Modules (last updated September 12, 2026).
2010. Darij Grinberg. Witt#5d: Analoga of integrality criteria for radical Witt polynomials (last updated September 12, 2026).
2010. Darij Grinberg. Witt#5e: Generalizing integrality theorems for ghost-Witt vectors (last updated September 12, 2026).
2009. Darij Grinberg. An inequality involving 2n numbers (last updated August 22, 2007).
2009. Darij Grinberg. Math Time problem proposal #1 (with solution) (last updated December 5, 2010).
2009. Darij Grinberg. Proof of a CWMO problem generalized (last updated September 7, 2009).
2008. Darij Grinberg. Generalizations of Popoviciu's inequality (last updated July 27, 2009). arXiv:0803.2958.
2008. Darij Grinberg. St. Petersburg 2003: An alternating sum of zero-sum subset numbers (last updated March 14, 2008).
2007. Darij Grinberg. An algebraic approach to Hall's matching theorem (last updated October 6, 2007).
2007. Darij Grinberg. The Vornicu-Schur inequality and its variations (last updated August 13, 2007).

Works: Elementary (Short)

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Darij Grinberg