Notch signaling mediates communication between cells and is essential for proper embryonic patterning and development. CSL is a DNA binding transcription factor that regulates transcription of Notch target genes by interacting with coregulators. Transcriptional activation requires the displacement of corepressors from CSL by the intracellular portion of the receptor Notch (NotchIC) and the recr...

Abstract For a peculiar family of double braid knots there is remarkable factorization formula for the coefficients differential (cyclotomic) expansion (DE), which nowadays widely used to construct exclusive Racah matrices S and $${\bar{S}}$$ S ¯ </mml:math...

We give a short proof inspired by Carter et al [1] that the 2–twist-spun trefoil is not isotopic to its orientation reverse. The proof uses a computer calculation of the third homology group of the three colour rack. We also give a new proof using the same calculation of the well-known fact that the left and right trefoil knots are not isotopic. AMS Classification 57Q45; 57M25, 57M27

A new classification theorem for links by the authors and Roger Fenn leads to computable link invariants. As an illustration we distinguish the left and right trefoils and recover the result of Carter et al that the 2-twist-spun trefoil is not isotopic to its orientation reverse. We sketch the proof the classification theorem. Full details will appear elsewhere AMS Classification 57Q45; 57M25, ...

The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is analyzed.