KaydedilenlerDerginizi ekleyin

Dergiler / Journal of Universal Mathematics / 2026 / Cilt: 7 Sayı: 2

SOME COLORING RESULTS ON SPECIAL SEMIGROUPS OBTAINED FROM PARTICULAR KNOTS

Umut Esen(KAHRAMANMARAS SUTCU IMAM UNIVERSITY)0000-0001-9697-8502
Ahmet Sinan Çevik(SELÇUK ÜNİVERSİTESİ)0000-0002-7539-5065
Mehmet Çitil(KAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİ)0000-0003-3899-3434
Sayfa
113–127
Yayın Tarihi
2024-07-31
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, for different knots K1 and K2 , we establish one can obtain a homomorphism or an isomorphism from the different knot semigroups K1S and K2S to the same alternating sum semigroup AS(Zn, B)

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:For a coloring set B ⊆ Zn, by considering the Fox n-coloring of any knot K and using the knot semigroup KS, we show that the set B is actually the same with the set C in the alternating sum semigroup AS(Zn, C).
📊
Temel Bulgular & Veri:Then, by adapting some results on Fox n-colorings to AS(Zn, B), we obtain some new results over this semigroup.
💡
Sonuç & Katkı:Moreover, for different knots K1 and K2 , we establish one can obtain a homomorphism or an isomorphism from the different knot semigroups K1S and K2S to the same alternating sum semigroup AS(Zn, B)
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Knot Theory · Semi Group · Quandle

Abstract

Abstract. For a coloring set B ⊆ Zn, by considering the Fox n-coloring of any knot K and using the knot semigroup KS, we show that the set B is actually the same with the set C in the alternating sum semigroup AS(Zn, C). Then, by adapting some results on Fox n-colorings to AS(Zn, B), we obtain some new results over this semigroup. In addition, we present the existence of different homomorphisms (or different isomorphisms in some cases) between the semigroups KS and AS(Zn, B), and then obtained the number of homomorphisms is in fact a knot invariant. Moreover, for different knots K1 and K2 , we establish one can obtain a homomorphism or an isomorphism from the different knot semigroups K1S and K2S to the same alternating sum semigroup AS(Zn, B)

🔖

Bu Makaleye Atıf Yap

Esen, U., Çevik, A. S., Çitil, M. (2024). SOME COLORING RESULTS ON SPECIAL SEMIGROUPS OBTAINED FROM PARTICULAR KNOTS. Journal of Universal Mathematics, Cilt: 7 Sayı: 2, 113–127. https://doi.org/10.33773/jum.1504811

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (19)

  1. C. C. Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, (2004).
  2. J. W. Alexander, Topological invariants of knots and links, Trans. Am. Math. Soc., Vol.30, pp.275-306 (1923).
  3. P. Andersson, The color invariant for knots and links, Amer. Math. Monthly, Vol.5, No.102, pp.442-448 (1995).
  4. Y. Bae, Coloring link diagrams by Alexander quandles, Journal of Knot Theory and Its Ramifications, Vol.21, No.10, pp.13 (2012).
  5. A. L. Breiland, L. Oesper, L. Taalman, p-coloring Classes of Torus Knots, Missouri J. Math. Sci., Vol.21, pp.120-126 (2009).
  6. K. Brownell, K. O'Neil, L. Taalman, Counting m-coloring classes of knots and links, Pi Mu Epsilon Journal, Vol.12, No.5, pp.265-278 (2005).
  7. W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman, Quandle Colorings of Knots and Applications, Journal of Knot Theory and its Ramifications, Vol.23, No.6, (2014).
  8. R. H. Crowell, R. H. Fox, Introduction to Knot Theory, Springer, (1977).
  9. M. Elhamdadi, S. Nelson, Quandles: An Introduction to the Algebra of Knots, AMS Book Series, Vol.74, (2015).
  10. D. Joyce, A Classifying Invariant of Knots, The Knot quandle, Journal of Pure and Applied Algebra, Vol.23, pp.37-65 (1982).
  11. L. H. Kauffman, Formal Knot Theory, Dover Publications, (2006).
  12. A. Kawauchi, A Survey of Knot Theory, Springer, (1996).
  13. W. B. R. Lickorish, An introduction to Knot Theory, Springer, (1997).
  14. T. Mochizuki, The Third Cohomology Groups of Dihedral Quandles, J. Knot Theory Ramifications, Vol.20, No.7, pp.1041-1057 (2011).
  15. K. Murasugi, Classical Knot Invariants and Elementary Number Theory, Contemporary Mathematics, pp.167-196, (2006).
  16. O. Nanyes, An Elementary Proof that the Borromean Rings are Non-Splittable, The American Mathematical Monthly, Vol.8, No.100, pp.786-789 (1993).
  17. D. Rolfsen, Knots and links, AMS Chelsea Pub, (2003).
  18. A. Vernitski, Describing semigroups with defining relations of the form xy = yz and yx = zy and connections with knot theory, Semigroup Forum, Vol.93, No.2, pp.387-402 (2016).
  19. N. Yoko, On the Alexander polynomials of pretzel links L, Kobe J. Math, Vol.2, pp.167-177 (1987).