Let F∗ n be the set of Boolean functions depending on all n variables. We prove that for any f ∈ F∗ n, f |xi=0 or f |xi=1 depends on the remaining n − 1 variables, for some variable xi. This existent result suggests a possible way to deal with general Boolean functions via its subfunctions of some restrictions. As an application, we consider the degree lower bound of representing polynomials ov...

Let n ≥ 2 and Tn be the space of n × n real skew-symmetric matrices. For each θ ∈ Tn the corresponding n-dimensional noncommutative torus Aθ is defined as the universal C-algebra generated by unitaries U1, · · · , Un satisfying the relation UkUj = e(θkj)UjUk, where e(t) = e. Noncommutative tori are one of the canonical examples in noncommutative differential geometry [12, 2]. One may also consi...

We introduce the maximumskew-symmetric ow problem which generalizes ow and matching problems. We develop a theory of skew-symmetric ows that is parallel to the classical ow theory. We use the newly developed theory to extend, in a natural way, the blocking ow method of Dinitz to the skew-symmetric ow case. In the special case of the skew-symmetric ow problem that corresponds to cardinality matc...

The study contributes to the cross-linguistic discussion on the prosodic correlates and categorial status of contrastive focus. It brings in data from Estonian, a flexible word order language where the prosodic expression of Information Structure has been very little studied. The study compares narrow contrastive focus with narrow and broad information focus in semi-spontaneous production data,...

Let M”= F-'(m,) be the preimage of the monomial symmetric function m, under F. We give an interpretation of M” in terms of certain combinatorial structures called I-domino tabloids. Using this interpretation, a number of properties of M” can be derived. The combinatorial interpretation of the preimage of the so called forgotten basis of Doubilet and Rota can also be obtained by similar techniques.

i=1 ti−1 (1+· · ·+qμi−1). In [8] Garsia-Tesler proved that if γ is a partition of k and λ = (n−k, γ) is a partition of n, then there is a unique symmetric polynomial kγ(x; q, t) of degree ≤ k with the property that K̃λμ(q, t) = kγ [Bμ(q, t); q, t] holds true for all partitions μ. It was shown there that these polynomials have Schur function expansions of the form kγ(x; q, t) = ∑ |ρ|≤|γ| Sλ(x) kρ...

It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton’s identities. In this work, by further exploring Newton’s identities, we discover a binomial decomposition rule for composite elementary symmetric polynomials. Utilizing this decomposition rule, we solve three types of systems of composite power...

1. Unitary Geometry on Exceptional Cartan Domains In 1935, E.Cartan classified all symmetric bounded domains. He prived that there exit only six types of irreducible bounded symmetric domains in C. They can be realized as follows: RI(m,n) = {Z ∈ Cmn|I − ZZ ′ > 0, Z − (m,n) matrix} RIIp = {Z ∈ Cp(p+1)/2|I − ZZ ′ > 0, Z − symmetric matric of degree p} RIIIq = {Z ∈ Cq(q−1)/2|I − ZZ ′ > 0, Z − skew...

Abstract. This paper will introduce noncommutative analogs of monomial symmetric functions and fundamental noncommutative symmetric functions. The expansion of ribbon Schur functions in both of these basis is nonnegative. With these functions at hand, one can derive a noncommutative Cauchy identity as well as study a noncommutative scalar product implied by Cauchy identity. This scalar product ...

We show how the superembedding formalism can be applied to construct manifestly kappasymmetric higher derivative corrections for the D9-brane. We also show that all correction terms appear at even powers of the fundamental length scale l. We explicitly construct the first potential correction, which corresponds to the kappa-symmetric version of the ∂4F 4, which one finds from the four-point amp...