We present an algorithm for computing A-annihilated elements of the form QI[1] in H*QS0 where I runs through admissible sequences of positive excess. This is algorithm with polynomial time complexity to address a sub-problem of an unsolved problem in algebraic topology known as the hit problem of Peterson which is likely to be NP-hard.
1. Edward B. Curtis.The Dyer-Lashof algebra and the Λ-algebra. Ill. J. Math., 19(1975), 231–246.
2. A. S. Janfada and R. M. W. Wood. The hit problem for symmetric polynomials over the Steenrod algebra. Math. Proc. Cambridge Philos. Soc., 133(2) (2002), 295–303.
3. A.S. Janfada and R.M.W. Wood. Generating H∗(BO(3); F32) as a module over the Steenrod algebra. Math. Proc. Camb. Philos. Soc., 134(2)(2003), 239–258.
4. Stewart Priddy. Dyer-Lashof operations for the classifying spaces of certain matrix groups. Quart. J. Math. Oxford Ser. (2), 26(102) (1975), 179–193.
5. Grant Walker and Reginald M. W. Wood. Polynomials and the mod 2 Steenrod algebra. Vol. 1. The Peterson hit problem, volume 441 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2018.
6. Grant Walker and Reginald M. W. Wood. Polynomials and the mod 2 Steenrod algebra. Vol. 2. Representations of GL(n; F2), volume 442 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2018.
7. Robert J. Wellington. The A-algebra H∗Ωn+1Σn+1X, the Dyer-Lashof algebra, and the Λ-algebra. 1977. Thesis (Ph.D.) The University of Chicago.
8. Robert J. Wellington. The unstable Adams spectral sequence for free iterated loop spaces. Mem. Am. Math. Soc., 36(258):225, 1982.
9. R. M. W. Wood. Hit problems and the Steenrod algebra. Lecture notes, University of Ioan- nina, Greece, June 2000.
10. Hadi Zare. The Dyer-Lashof algebra and the hit problems. (appendix by HasanZadeh, Seyyed Mohammad Ali). New York J. Math., 27(2021), 1134–1172.
Zare, H., & Hasanzadeh, S. M. (2023). An algorithm for constructing A-annihilated admissible monomials in the Dyer-Lashof algebra. Journal of Finsler Geometry and its Applications, 4(2), 58-63. doi: 10.22098/jfga.2023.13656.1098
MLA
Hadi Zare; Seyyed Mohammadali Hasanzadeh. "An algorithm for constructing A-annihilated admissible monomials in the Dyer-Lashof algebra", Journal of Finsler Geometry and its Applications, 4, 2, 2023, 58-63. doi: 10.22098/jfga.2023.13656.1098
HARVARD
Zare, H., Hasanzadeh, S. M. (2023). 'An algorithm for constructing A-annihilated admissible monomials in the Dyer-Lashof algebra', Journal of Finsler Geometry and its Applications, 4(2), pp. 58-63. doi: 10.22098/jfga.2023.13656.1098
VANCOUVER
Zare, H., Hasanzadeh, S. M. An algorithm for constructing A-annihilated admissible monomials in the Dyer-Lashof algebra. Journal of Finsler Geometry and its Applications, 2023; 4(2): 58-63. doi: 10.22098/jfga.2023.13656.1098
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