In 1957, N. G. de Bruijn showed that the symmetric group Sym(Ω) on an infinite set Ω contains a free subgroup on 2 generators, and proved a more general statement, a sample consequence of which is that for any group A of cardinality ≤ card(Ω), the group Sym(Ω) contains a coproduct of 2 copies of A, not only in the variety of all groups, but in any variety of groups to which A belongs. His key l...

We investigate the connection between Tamari lattices and the Thompson group F , summarized in the fact that F is a group of fractions for a certain monoid F sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F sym. As an application, we show tha...

lation, does not produce a sufficient clean differ'4B-m ence image for text recognition. In analogy to this subtraction we propose the The proposed method has the aim to name 'symbolic subtraction' for our new separate the filled in (typed or handwritten) approach in this paper: the 'symbolic difference' information in a form, from the fixed preprinted Sym(FF)-Sym(BF) means the recognition of t...

We study some dynamical aspects of the correspondence between strings in AdS space and external heavy quarks in N = 4 SYM. Specifically, by examining waves propagating on such strings, we make some plausible (and some surprising) inferences about the time-dependent fields produced by oscillating quarks in the stronglycoupled gauge theory. We point out a puzzle regarding energy conservation in t...

One-loop maximal helicity violating (MHV) amplitudes in N = 4 super YangMills (SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and Witten (CSW). The relations between leading Nc amplitudes An;1 and sub-leading amplitudes An;c obtained by the CSW prescription are found to be identical to those obtained from conventional field theory calculations. Combining with existing re...

In the aim of attacking the first conjecture of Montgomery-Vaughan on the distribution of values of the automorphic symmetric power L-functions at 1, we study the distribution function of the truncated random Euler products L(1, sym m g ♮ (ω), y) := p≤y det I − p −1 sym m g ♮ p (ω) −1 , where g ♮ (ω) := {g ♮ p (ω)} p is a sequence of independent random variables, defined in probability space Ω ...

We determine the exact beta function and a RG flow Lyapunov function for N = 2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg–Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non–perturbative identity relating the u–modulus and the superconformal anomaly, indicate the existence of a four dimen...

As a non-trivial check of the non-supersymmetric gauge/gravity duality, we use a near-extremal black brane background to compute the retarded Green’s functions of the stress-energy tensor in N = 4 super-Yang-Mills (SYM) theory at finite temperature. For the long-distance, low-frequency modes of the diagonal components of the stress-energy tensor, hydrodynamics predicts the existence of a pole i...

We consider the solution of complex symmetric shifted linear systems. Such systems arise in largescale electronic structure simulations, and there is a strong need of algorithms for their fast solution. With the aim of solving the systems efficiently, we consider a special case of the QMR method for non-Hermitian shifted linear systems and propose its weighted quasi-minimal residual approach. A...

We initiate study of the Terwilliger algebra and related semidefinite programming techniques for the conjugacy scheme of the symmetric group Sym(n). In particular, we compute orbits of ordered pairs on Sym(n) acted upon by conjugation and inversion, explore a block di-agonalization of the associated algebra, and obtain improved upper bounds on the size M (n, d) of permutation codes of lengths u...