Research works

Works containing new results or ideas (novelty level 4 or higher). A novelty level of 4 roughly corresponds to new results and 5 to new concepts or ideas.

68 records
2026. GPT-5.6 Sol, Darij Grinberg. A counterexample to the Burman--Kulishov conjecture on Lie elements (last updated August 16, 2026).
2026. Sarah Brauner, Patricia Commins, Darij Grinberg, Franco Saliola. A left ideal Gelfand model for the symmetric group (last updated April 15, 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-5.6 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, 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. GPT-5.6 Sol, Darij Grinberg. On Injectivity of Coalgebra Morphisms (last updated August 18, 2026).
2026. Benjamin Adenbaum, Darij Grinberg. On the q-Poincaré sum of a Coxeter group (last updated July 11, 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, Ekaterina A. Vassilieva. The left-to-right minima basis of the group algebra of the symmetric group (last updated June 1, 2026). arXiv:2601.02952.
2026. Darij Grinberg. The representation theory of somewhere-to-below shuffles (last updated April 17, 2026). arXiv:2508.00752. The Electronic Journal of Combinatorics, 33, 2026, issue 2, P2.55.
2025. Darij Grinberg. An introduction to the algebra of rings and fields (last updated September 12, 2026). arXiv:2508.13165.
2025. Darij Grinberg. Rook sums in the symmetric group algebra (last updated July 11, 2026). arXiv:2507.22386.
2025. Sarah Brauner, Patricia Commins, Darij Grinberg, Franco Saliola. The q-deformed random-to-random family in the Hecke algebra (last updated November 17, 2025). arXiv:2503.17580.
2025. Darij Grinberg, Jonathan Parlett. Top to random and reverse: analysis of a new descent algebra shuffle (last updated August 8, 2025). arXiv:2508.06740.
2024. Darij Grinberg. A Solomon Mackey formula for graded bialgebras (last updated July 24, 2026). arXiv:2401.14648.
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, Ekaterina A. Vassilieva. The enriched q-monomial basis of the quasisymmetric functions (last updated June 5, 2026). arXiv:2309.01118. The Electronic Journal of Combinatorics, 31, 2024, issue 4, P4.20.
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. Commutator nilpotency for somewhere-to-below shuffles (last updated April 16, 2026). arXiv:2309.05340.
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. On the square of the antipode in a connected filtered Hopf algebra (last updated June 16, 2026). arXiv:2109.02101v2. Communications in Mathematics 31 (2023), issue 1, article 10431.
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, 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. 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 Pelletier--Ressayre hidden symmetry for Littlewood--Richardson coefficients (last updated June 15, 2026). arXiv:2008.06128. Combinatorial Theory 1 (2021), no. 16.
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. Erik Aas, Darij Grinberg, Travis Scrimshaw. Multiline queues with spectral parameters (last updated April 15, 2026). arXiv:1810.08157. Communications in Mathematical Physics 374 (2020), no. 3, pp. 1743--1786.
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. Gérard Duchamp, Darij Grinberg, Vincel Minh. Three variations on the linear independence of grouplikes in a coalgebra (last updated July 3, 2026). arXiv:2009.10970.
2019. Darij Grinberg. A basis for a quotient of symmetric polynomials (last updated May 24, 2026). arXiv:1910.00207.
2019. Darij Grinberg. Commutators, matrices and an identity of Copeland (last updated June 17, 2026). arXiv:1908.09179.
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, 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. Shuffle-compatible permutation statistics II: the exterior peak set (last updated September 1, 2026). arXiv:1806.04114. Electronic Journal of Combinatorics 25 (2018), Issue 4, Paper #P4.17.
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. Double posets and the antipode of QSym (extended abstract) (last updated February 19, 2017).
2017. Darij Grinberg. Dual immaculate creation operators and a dendriform algebra structure on the quasisymmetric functions (last updated August 31, 2026). arXiv:1410.0079. Canadian Journal of Mathematics 69 (2017), no. 1, pp. 21--53.
2017. Darij Grinberg, Alexander Postnikov. Proof of a conjecture of Bergeron, Ceballos and Labbé (last updated June 19, 2026). arXiv:1603.03138. New York Journal of Mathematics 23 (2017), pp. 1581--1610.
2017. Darij Grinberg. t-unique reductions for Mészáros's subdivision algebra (last updated June 19, 2026). arXiv:1704.00839. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 14 (2018), 078.
2016. Darij Grinberg, Karthik Karnik, Anya Zhang. A generalization of Chio Pivotal Condensation (last updated May 7, 2026). arXiv:1606.08193.
2016. James Borger, Darij Grinberg. Boolean Witt vectors and an integral Edrei-Thoma theorem (last updated December 11, 2015). arXiv:1311.5031v4. Selecta Mathematica 22(2), pp. 595--629.
2016. Darij Grinberg. Do the symmetric functions have a function-field analogue? (last updated August 10, 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. 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. The Bernstein homomorphism via Aguiar-Bergeron-Sottile universality (last updated June 12, 2026). arXiv:1604.02969.
2015. Darij Grinberg. The signed random-to-top operator on tensor space (last updated May 21, 2026). arXiv:1505.01201.
2014. Darij Grinberg, Victor Reiner. Hopf Algebras in Combinatorics (last updated September 6, 2026). arXiv:1409.8356.
2013. Darij Grinberg. Mathematical Reflections problem U275 (last updated June 4, 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. Darij Grinberg. Zeckendorf family identities generalized (last updated April 13, 2026). arXiv:1103.4507.
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).

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Darij Grinberg