پیشنویس:گروه متقارن آفین: تفاوت میان نسخهها
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[[رده:نظریه نمایش]] |
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==اثر های ذکر شده== |
==اثر های ذکر شده== |
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* {{citation|title = Bijective projections on parabolic quotients of affine Weyl groups | last1 = Beazley |first1 = Elizabeth |last2 = Nichols | first2 = Margaret |last3 = Park|first3 = Min Hae |last4 = Shi|first4 = XiaoLin |last5 = Youcis|first5 = Alexander | journal = [[J. Algebr. Comb.]] | year = 2015 | volume = 41 | issue = 4 | pages = 911–948|doi=10.1007/s10801-014-0559-9|doi-access = free }} |
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* {{citation| title = Matrix-ball construction of affine Robinson-Schensted correspondence | last1 = Chmutov | first1 = Michael | last2 = Pylyavskyy | first2 = Pavlo | last3 = Yudovina |first3 = Elena | journal = [[Selecta Math.]] |series=New Series | volume = 24 | issue = 2 | year = 2018 | pages = 667–750 | doi = 10.1007/s00029-018-0402-6| arxiv = 1511.05861 | s2cid = 119086049 }} |
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* {{citation |title=On 321-Avoiding Permutations in Affine Weyl Groups |last=Green |first=R.M. |journal=[[J. Algebr. Comb.]] |year=2002 |volume=15 |issue=3 |pages=241–252 |doi=10.1023/A:1015012524524 |s2cid=10583938 |doi-access=free}} |
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* {{citation|title = The enumeration of fully commutative affine permutations | last1 = Hanusa | first1 = Christopher R.H. | last2 = Jones | first2 = Brant C. | journal = [[Eur. J. Comb.]] | volume = 31 | issue = 5 | year = 2010 | pages = 1342–1359 | doi = 10.1016/j.ejc.2009.11.010| arxiv = 0907.0709 | s2cid = 789357 }} |
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* {{citation |title=Abacus models for parabolic quotients of affine Weyl groups |last1=Hanusa |first1=Christopher R.H. |s2cid=47583179 |last2=Jones |first2=Brant C. |journal=[[J. Algebra]] |volume=361 |year=2012 |pages=134–162 |arxiv=1105.5333v2 |doi=10.1016/j.jalgebra.2012.03.029 |doi-access=free}} |
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* {{citation |title=Reflection groups and invariant theory |last=Kane |first=Richard |publisher=Springer-Verlag |series=CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC |year=2001 |isbn=0-387-98979-X |s2cid=119694827 |doi=10.1007/978-1-4757-3542-0}} |
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* {{citation |title=A geometric and algebraic description of annular braid groups |last1=Kent, IV |first1=Richard P. |s2cid=13593688 |last2=Peifer |first2=David |year=2002 |department=International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000) |journal=[[Internat. J. Algebra Comput.]] |volume=12 |issue=1–2 |pages=85–97 |doi=10.1142/S0218196702000997}} |
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* {{citation |title=Positroid varieties: juggling and geometry |last1=Knutson |first1=Allen |author1-link=Allen Knutson |s2cid=16108179 |last2=Lam |first2=Thomas |last3=Speyer |first3=David E. |journal=[[Compositio Mathematica]] |volume=149 |year=2013 |issue=10 |pages=1710–1752 |doi=10.1112/S0010437X13007240 |doi-access=free}} |
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* {{citation |title=The shape of a random affine Weyl group element and random core partitions |last=Lam |first=Thomas |journal=[[Ann. Probab.]] |volume=43 |year=2015 |issue=4 |pages=1643–1662 |arxiv=1102.4405v3 |doi=10.1214/14-AOP915 |s2cid=119691692 |doi-access=free}} |
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* {{citation | title = Tableaux on <math>k+1</math>-cores, reduced words for affine permutations, and <math>k</math>-Schur expansions | last1 = Lapointe | first1 = Luc | last2 = Morse | first2 = Jennifer | author2-link = Jennifer Morse (mathematician) | journal = [[J. Combin. Theory Ser. A]] | volume = 112 | issue = 1 | year = 2005 | pages = 44–81 | doi = 10.1016/j.jcta.2005.01.003| s2cid = 161241 | doi-access = free }} |
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نسخهٔ ۲۲ دسامبر ۲۰۲۳، ساعت ۱۱:۳۱
گروههای متقارن وابسته شاخهای از جبر در ریاضیات است که به مطالعه و توصیف تقارنهای محور اعداد و کاشی کاری مثلثی منظم صفحه و اجسام با ابعاد بالاتر مرتبط میپردازد. علاوه بر این توصیف هندسی، گروههای متقارن وابسته به روش دیگری نیز تعریف میشوند. مثلا:به عنوان مجموعهای از جایگشتهای (باز چینی) اعداد صحیح که در زمان خاصی بهصورت متناوب هستند یا به اصطلاح تخصصی تر، به عنوان گروه با مولد و روابط (تعیین گروه با مولد و روابط بین آنها) است که در ترکیبیات و نظریهٔ نمایش بررسی میشوند. یک گروه متقارن محدود، شامل همه جایگشتهای یک مجموعه متناهی است. هر گروه متقارن وابسته، توسیع گروهی از یک گروه متقارن محدود است. بسیاری از ویژگیهای ترکیبی مهم گروههای متقارن محدود میتواند به گروههای متقارن وابسته متناظر تعمیم داده شود. آمار جایشگت (تصادفی) مانند جایگشت و وراونگی را میتوان در وابسته تعریف کرد. همانطور که در حالت محدود، تعاریف ترکیبی طبیعی برای این آمار نیز تفسیر هندسی دارند. گروههای متقارن وابسته روابط نزدیکی با سایر موضوعات ریاضی دارند، از جمله الگو(ترفند)های شعبدهبازی و گروههای بازتابی پیچیده خاص است. بسیاری از ویژگیهای ترکیبی و هندسی آنها به خانواده گستردهتر گروههای کاکسیتر تعمیم داده میشود.
تعریف ها
گروه متقارن وابسته ممکن است به عنوان معادل یک گروه انتزاعی، توسط مولدها و روابط تعریف شود.یا از نظر مدل های هندسی به هم چسبیده یا ترکیبی تعریف شود.[۱]
منابع
- ↑ Shi (1986), p. 66.
اثر های ذکر شده
- Allcock, Daniel (2002), "Braid pictures for Artin groups", Trans. Amer. Math. Soc., 354 (9): 3455–3474, doi:10.1090/S0002-9947-02-02944-6, S2CID 14473723
- Beazley, Elizabeth; Nichols, Margaret; Park, Min Hae; Shi, XiaoLin; Youcis, Alexander (2015), "Bijective projections on parabolic quotients of affine Weyl groups", J. Algebr. Comb., 41 (4): 911–948, doi:10.1007/s10801-014-0559-9
- Berg, Chris; Jones, Brant; Vazirani, Monica (2009), "A bijection on core partitions and a parabolic quotient of the affine symmetric group", J. Combin. Theory Ser. A, 116 (8): 1344–1360, arXiv:0804.1380, doi:10.1016/j.jcta.2009.03.013, S2CID 3032099
- Billey, Sara C.; Jockusch, William; Stanley, Richard P. (1993), "Some Combinatorial Properties of Schubert Polynomials", J. Algebr. Comb., 2 (4): 345–374, doi:10.1023/A:1022419800503, S2CID 8628113
- Björner, Anders; Brenti, Francesco (1996), "Affine permutations of type A", Electron. J. Combin., 3 (2): R18, doi:10.37236/1276, S2CID 2987208
- Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
- Cameron, Peter J. (1994), Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, doi:10.1017/CBO9780511803888, ISBN 978-0-521-45761-3, S2CID 115451799
- Charney, Ruth; Peifer, David (2003), "The -conjecture for the affine briad groups", Comment. Math. Helv., 78 (3): 584–600, doi:10.1007/S00014-003-0764-Y, S2CID 54016405
- Chmutov, Michael; Lewis, Joel Brewster; Pylyavskyy, Pavlo (2022), "An affine generalization of evacuation", Selecta Math., New Series, 28 (4): Paper 67, arXiv:1706.00471, doi:10.1007/s00029-022-00779-x, S2CID 119168718
- Chmutov, Michael; Frieden, Gabriel; Kim, Dongkwan; Lewis, Joel Brewster; Yudovina, Elena (2022), "Monodromy in Kazhdan-Lusztig cells in affine type A", Math. Annalen, 386 (3–4): 1891–1949, arXiv:1806.07429, doi:10.1007/s00208-022-02434-4, S2CID 119669284
- Chmutov, Michael; Pylyavskyy, Pavlo; Yudovina, Elena (2018), "Matrix-ball construction of affine Robinson-Schensted correspondence", Selecta Math., New Series, 24 (2): 667–750, arXiv:1511.05861, doi:10.1007/s00029-018-0402-6, S2CID 119086049
- Clark, Eric; Ehrenborg, Richard (2011), "Excedances of affine permutations", Advances in Applied Mathematics, 46 (1–4): 175–191, doi:10.1016/j.aam.2009.12.006, S2CID 15349463
- Coxeter, H.S.M. (1973), Regular Polytopes (3 ed.), Dover, ISBN 0-486-61480-8
- Crites, Andrew (2010), "Enumerating pattern avoidance for affine permutations", Electron. J. Combin., 17 (1): R127, arXiv:1002.1933, doi:10.37236/399, S2CID 15383510
- Ehrenborg, Richard; Readdy, Margaret (1996), "Juggling and applications to q-analogues", Discrete Math., 157 (1–3): 107–125, CiteSeerX 10.1.1.8.6684, doi:10.1016/S0012-365X(96)83010-X, S2CID 18149014
- Eriksson, Henrik; Eriksson, Kimmo (1998), "Affine Weyl groups as infinite permutations", Electron. J. Combin., 5: R18, doi:10.37236/1356, S2CID 218962
- Gallian, Joseph A. (2013), Contemporary Abstract Algebra (8th ed.), Brooks/Cole, ISBN 978-1-133-59970-8, LCCN 2012938179
- Green, R.M. (2002), "On 321-Avoiding Permutations in Affine Weyl Groups", J. Algebr. Comb., 15 (3): 241–252, doi:10.1023/A:1015012524524, S2CID 10583938
- Hanusa, Christopher R.H.; Jones, Brant C. (2010), "The enumeration of fully commutative affine permutations", Eur. J. Comb., 31 (5): 1342–1359, arXiv:0907.0709, doi:10.1016/j.ejc.2009.11.010, S2CID 789357
- Hanusa, Christopher R.H.; Jones, Brant C. (2012), "Abacus models for parabolic quotients of affine Weyl groups", J. Algebra, 361: 134–162, arXiv:1105.5333v2, doi:10.1016/j.jalgebra.2012.03.029, S2CID 47583179
- Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
- Kac, Victor G. (1990), Infinite-dimensional Lie algebras (PDF) (3rd ed.), Cambridge University Press, doi:10.1017/CBO9780511626234, ISBN 0-521-46693-8
- Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
- Kent, IV, Richard P.; Peifer, David (2002), "A geometric and algebraic description of annular braid groups", International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000), Internat. J. Algebra Comput., 12 (1–2): 85–97, doi:10.1142/S0218196702000997, S2CID 13593688
- Knutson, Allen; Lam, Thomas; Speyer, David E. (2013), "Positroid varieties: juggling and geometry", Compositio Mathematica, 149 (10): 1710–1752, doi:10.1112/S0010437X13007240, S2CID 16108179
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