A classical result states that the determinant of an alternating link is equal to the number of spanning trees in a checkerboard graph of an alternating connected projection of the link. We generalize this result to show that the determinant is the alternating sum of the number of quasi-trees of genus j of the dessin of a non-alternating link. Furthermore, we obtain formulas for coefficients of...

In this paper we generalize the concept of alternating knots to alternating graphs and show that every abstract graph has a spatial embedding that is alternating. We also prove that every spatial graph is a subgraph of an alternating graph. We define n-composition for spatial graphs and generalize the results of Menasco on alternating knots to show that an alternating graph is n-composite for n...

The compellingness of the interaction between vision and auditory localization (the ventriloquist effect) was investigated using a discrimination task. A tone sequence was presented either from the same location or from two locations that alternated along the horizontal plane. In synchrony with the tones, lights were presented either at the same or at alternating locations. Subjects had to deci...

A symplectic alternating algebra (SAA) is a symplectic vector space L, whose associated alternating form is non-degenerate, that is furthermore equipped with a binary alternating product · : L× L 7→ L with the extra requirement that (x · y, z) = (y · z, x) for all x, y, z ∈ L. This condition can be expressed equivalently by saying that (u · x, v) = (u, v · x) for all u, v, x ∈ L or in other wor...

The well-known Wolstenholme’s Theorem says that for every prime p > 3 the (p−1)-st partial sum of the harmonic series is congruent to 0 modulo p2. If one replaces the harmonic series by ∑ k≥1 1/n for k even, then the modulus has to be changed from p2 to just p. One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partia...