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We study the problem of representing symmetric Boolean functions as symmetric polynomials over . We show an equivalence between such representations and simultaneous communication protocols. Computing a function with a polynomial of degree modulo is equivalent to a two player simultaneous protocol for computing where one player is given the first digits of the weight in base and the other is gi...

We describe a recursive algorithm that produces an integral basis for the centre of the Hecke algebra of type A consisting of linear combinations of monomial symmetric polynomials of Jucys–Murphy elements. We also discuss the existence of integral bases for the centre of the Hecke algebra that consist solely of monomial symmetric polynomials of Jucys–Murphy elements. Finally, for n = 3, we show...

Generalizing the classical Capelli identity has recently attracted a lot of interest ([HU], [Ok], [Ol], [Sa], [WUN]). In several of these papers it was realized, in various degrees of generality, that Capelli identities are connected with certain symmetric polynomials which are characterized by their vanishing at certain points. From this point of view, these polynomials have been constructed b...

By the fundamental theorem of symmetric polynomials, if P ∈ Q[X1, . . . , Xn] is symmetric, then it can be written P = Q(σ1, . . . , σn), where σ1, . . . , σn are the elementary symmetric polynomials in n variables, and Q is in Q[S1, . . . , Sn]. We investigate the complexity properties of this construction in the straight-line program model, showing that the complexity of evaluation of Q depen...

In this paper we introduce a family of polynomials indexed by pairs of partitions and show that if these polynomials are self–orthogonal then the centre of the Iwahori–Hecke algebra of the symmetric group is precisely the set of symmetric polynomials in the Murphy operators.

We prove a nonsymmetric analogue of a formula of Kato and Lusztig which describes the coefficients of the expansion of irreducible Weyl characters in terms of (degenerate) symmetric Macdonald polynomials as certain Kazhdan–Lusztig polynomials. We also establish precise polynomiality results for coefficients of symmetric and nonsymmetric Macdonald polynomials and a version of Demazure’s characte...

In this paper we introduce a family of polynomials indexed by pairs of partitions and show that if these polynomials are self-orthogonal then the centre of the Iwahori-Hecke algebra of the symmetric group is precisely the set of symmetric polynomials in the Murphy operators.

Background material on α-shift radix systems and α-CNS polynomials is collected. Symmetric CNS trinomials of the shape Xd + bX + c (d > 2) are characterized, thereby extending known results on quadratic symmetric CNS polynomials.