The stable conjugation-invariant word norm is rational in free groups
HTML articles powered by AMS MathViewer
- by Henry Jaspars;
- Proc. Amer. Math. Soc. 152 (2024), 2403-2412
- DOI: https://doi.org/10.1090/proc/16786
- Published electronically: April 25, 2024
- HTML | PDF | Request permission
Abstract:
We establish the rationality of the stable conjugation-invariant word norm on free groups and virtually free Coxeter groups.References
- Y. Bar-Hillel, M. Perles, and E. Shamir, On formal properties of simple phrase structure grammars, Z. Phonetik Sprachwiss. Kommunikat. 14 (1961), 143–172. MR 151376
- Michael Brandenbursky, Światosław R. Gal, Jarek Kędra, and MichałMarcinkowski, The cancellation norm and the geometry of bi-invariant word metrics, Glasg. Math. J. 58 (2016), no. 1, 153–176. MR 3426433, DOI 10.1017/S0017089515000129
- Michael Brandenbursky, Jarek Kędra, and Egor Shelukhin, On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus, Commun. Contemp. Math. 20 (2018), no. 2, 1750042, 27. MR 3730755, DOI 10.1142/S0219199717500420
- Danny Calegari, scl, MSJ Memoirs, vol. 20, Mathematical Society of Japan, Tokyo, 2009. MR 2527432, DOI 10.1142/e018
- Danny Calegari, Stable commutator length is rational in free groups, J. Amer. Math. Soc. 22 (2009), no. 4, 941–961. MR 2525776, DOI 10.1090/S0894-0347-09-00634-1
- Danny Calegari and Dongping Zhuang, Stable $W$-length, Topology and geometry in dimension three, Contemp. Math., vol. 560, Amer. Math. Soc., Providence, RI, 2011, pp. 145–169. MR 2866929, DOI 10.1090/conm/560/11097
- N. Chomsky, Three models for the description of language, IRE Trans. Inform. Theory, 1956, pp. 113–124.
- Michael W. Davis, The geometry and topology of Coxeter groups, London Mathematical Society Monographs Series, vol. 32, Princeton University Press, Princeton, NJ, 2008. MR 2360474
- Volker Diekert and Armin Weiß, Context-free groups and their structure trees, Internat. J. Algebra Comput. 23 (2013), no. 3, 611–642. MR 3048114, DOI 10.1142/S0218196713500124
- Matthew J. Dyer, On minimal lengths of expressions of Coxeter group elements as products of reflections, Proc. Amer. Math. Soc. 129 (2001), no. 9, 2591–2595. MR 1838781, DOI 10.1090/S0002-9939-01-05876-2
- Siddhartha Gadgil, Conjugacy invariant pseudo-norms, representability and RNA secondary structures, Indian J. Pure Appl. Math. 42 (2011), no. 4, 225–237. MR 2845645, DOI 10.1007/s13226-011-0015-7
- Harold Greenberg, An algorithm for the periodic solutions in the knapsack problem, J. Math. Anal. Appl. 111 (1985), no. 2, 327–331. MR 813212, DOI 10.1016/0022-247X(85)90219-7
- M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295. MR 1253544
- J. E. Hopcroft, R. Motwani, and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 2 edition, 2001.
- Joel Brewster Lewis, Jon McCammond, T. Kyle Petersen, and Petra Schwer, Computing reflection length in an affine Coxeter group, Trans. Amer. Math. Soc. 371 (2019), no. 6, 4097–4127. MR 3917218, DOI 10.1090/tran/7472
- L. Y. Liu and P. Weiner, A characterization of semilinear sets, J. Comput. System Sci. 4 (1970), 299–307. MR 269448, DOI 10.1016/S0022-0000(70)80015-0
- Jon McCammond and T. Kyle Petersen, Bounding reflection length in an affine Coxeter group, J. Algebraic Combin. 34 (2011), no. 4, 711–719. MR 2842917, DOI 10.1007/s10801-011-0289-1
- Dusa McDuff and Dietmar Salamon, Introduction to symplectic topology, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1998. MR 1698616
- David E. Muller and Paul E. Schupp, Groups, the theory of ends, and context-free languages, J. Comput. System Sci. 26 (1983), no. 3, 295–310. MR 710250, DOI 10.1016/0022-0000(83)90003-X
- Rohit J. Parikh, On context-free languages, J. Assoc. Comput. Mach. 13 (1966), 570–581. MR 209093, DOI 10.1145/321356.321364
- Hans Jürgen Prömel, Induced partition properties of combinatorial cubes, J. Combin. Theory Ser. A 39 (1985), no. 2, 177–208. MR 793270, DOI 10.1016/0097-3165(85)90036-6
- Herbert S. Wilf, generatingfunctionology, Academic Press, Inc., Boston, MA, 1990. MR 1034250
- Dongping Zhuang, Irrational stable commutator length in finitely presented groups, J. Mod. Dyn. 2 (2008), no. 3, 499–507. MR 2417483, DOI 10.3934/jmd.2008.2.499
Bibliographic Information
- Henry Jaspars
- Affiliation: Trinity College, Cambridge, CB2 1TQ, United Kingdom
- MR Author ID: 1575461
- ORCID: 0009-0009-8220-2629
- Email: hj388@cam.ac.uk
- Received by editor(s): April 28, 2023
- Received by editor(s) in revised form: December 11, 2023
- Published electronically: April 25, 2024
- Communicated by: Martin Liebeck
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2403-2412
- MSC (2020): Primary 20F65, 20E05; Secondary 68R15, 68Q45
- DOI: https://doi.org/10.1090/proc/16786
- MathSciNet review: 4741237