Max Loehr (1903–88)

128-136 Loehr Jan 6 rev.indd

The authors examined how timing accuracy in tapping sequences is influenced by sequential effects of preceding finger movements and biomechanical interdependencies among fingers. Skilled pianists tapped sequences at 3 rates; in each sequence, a finger whose motion was more or less independent of other fingers’ motion was preceded by a finger to which it was more or less coupled. Less independen...

Haglund-haiman-loehr Type Formulas for Hall-littlewood Polynomials of Type B and C

In previous work we showed that two apparently unrelated formulas for the Hall-Littlewood polynomials of type A are, in fact, closely related. The first is the tableau formula obtained by specializing q = 0 in the HaglundHaiman-Loehr formula for Macdonald polynomials. The second is the type A instance of Schwer’s formula (rephrased and rederived by Ram) for HallLittlewood polynomials of arbitra...

Random Max 2-sat and Max Cut

Given a 2-SAT formula F consisting of n variables and b n random clauses, what is the largest number of clauses maxF satisfiable by a single assignment of the variables? We bound the answer away from the trivial bounds of 34 n and n. We prove that for < 1, the expected number of clauses satisfiable is b n o(1); for large , it is ( 34 + (p ))n; for = 1 + ", it is at least (1 + " O("3))n and at m...

Modelling Max-CSP as Partial Max-SAT

We define a number of original encodings that map MaxCSP instances into partial Max-SAT instances. Our encodings rely on the well-known direct and support encodings from CSP into SAT. Then, we report on an experimental investigation that was conducted to compare the performance profile of our encodings on random binary Max-CSP instances. Moreover, we define a new variant of the support encoding...

Max Wellington