TY - JOUR
T1 - ON QUASI-ALTERNATING KNOTS WITH SYMMETRIC UNION PRESENTATIONS
AU - Chbili, Nafaa
AU - Tanaka, Toshifumi
N1 - Publisher Copyright:
© 2025, Osaka University. All rights reserved.
PY - 2025/4
Y1 - 2025/4
N2 - There are only finitely many alternating symmetric unions for a given partial knot. In this paper, we give a formula for the Q-polynomial of a knot with the symmetric union presentation D ∪ D∗(m) and show that, if 2degQ(D) > degQ(D ∪ D∗ (∞)), then there are only finitely many quasi-alternating knots with the symmetric union presentation D ∪ D∗ (m) for any knot diagram D. We also give a formula for the Q-polynomial of a knot with the symmetric union presentation D ∪ D∗(m1, m2).
AB - There are only finitely many alternating symmetric unions for a given partial knot. In this paper, we give a formula for the Q-polynomial of a knot with the symmetric union presentation D ∪ D∗(m) and show that, if 2degQ(D) > degQ(D ∪ D∗ (∞)), then there are only finitely many quasi-alternating knots with the symmetric union presentation D ∪ D∗ (m) for any knot diagram D. We also give a formula for the Q-polynomial of a knot with the symmetric union presentation D ∪ D∗(m1, m2).
UR - https://www.scopus.com/pages/publications/105011614487
UR - https://www.scopus.com/pages/publications/105011614487#tab=citedBy
M3 - Article
AN - SCOPUS:105011614487
SN - 0030-6126
VL - 62
SP - 317
EP - 328
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
IS - 2
ER -