The Robinson–Schensted–Knuth bijection, denoted by RSK, is a bijection between sequences π of real numbers of length n ≥ 1 and ordered pairs 〈P,Q〉 where P = P (π) is a semi–standard tableau with entries π1, . . . , πn, Q = Q(π) is a standard Young tableau with entries one through n, and P and Q both have shape λ = λ(π) where |λ| = n. Schensted’s theorem, which has been generalized by Greene, st...

We performed Monte Carlo simulations of the two-dimensional qstate Potts model with q = 10, 15, and 20 to study the energy and magnetization cumulants in the ordered and disordered phase at the first-order transition point βt. By using very large systems of size 300× 300, 120× 120, and 80× 80 for q = 10, 15, and 20, respectively, our numerical estimates provide practically (up to unavoidable, b...

An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this ordered set can be computed in time O(n 2 log 2 n), where n = jLj. This paper is motivated by the problem of eeciently calculating and representing the congruence lattice Con L of a nite lattice L. Of cou...

Quantum Logic: A logic (血,←, þ), where the proof-theoretic and the semantic-consequence relations violate some characteristic classical principles like the distributivity of conjunction and disjunction. Adjoint: If A is a bounded operator on a Hilbert space , then the adjoint of A is the unique bounded operator A食 that satisfies (A~ φ) = (ψIA* φ) for all vectors ψ, φin the space. Algebraic Mode...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing, and the stat...

We consider a problem of shuffling a deck of cards with ordered labels. Namely we split the deck of N = kq cards (where t ≥ 1 is maximal) into k equally sized stacks and then take the top card off of each stack and sort them by the order of their labels and add them to the shuffled stack. We show how to find stacks of cards invariant and periodic under the shuffling. We also show when gcd(q, k)...

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing, and the stat...

We consider the problem of query evaluation for tuple independent probabilistic databases and Boolean conjunctive queries with inequalities but without self-joins. We approach this problem as a construction problem for ordered binary decision diagrams (OBDDs): Given a query q and a probabilistic database D, we construct in polynomial time an OBDD such that the probability of q(D) can be compute...

016405-1 We consider a two-dimensional itinerant antiferromagnet near a quantum-critical point. We show that, contrary to conventional wisdom, fermionic excitations in the ordered state are not the usual Fermi-liquid quasiparticles. Instead, down to very low frequencies, the fermionic self-energy varies as !2=3. This non-Fermi-liquid behavior originates in the coupling of fermions to the longit...