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Let $v(n)$ be the minimum number of voters with transitive preferences which are needed to generate any strong preference pattern (ties not allowed) on $n$ candidates. Let $k=\lfloor \log_2 n\rfloor$....
On Zudilin's q-question about Schmidt's problem
Schmidt’s problem q-binomial coefficients q-Pfaff-Saalschutz identity
2012/4/17
For any integer $r\geqslant 2$, using the $q$-Pfaff-Saalsch\"utz identity, we prove that there exists a (unique) sequence of Laurent polynomials $\{b^{(r)}_k(q)\}_{k=0}^\infty$ in $q$ with nonnegative...
Heuristic and exact solutions to the inverse power index problem for small voting bodies
electoral systems simple games weighted voting games square root rule Penrose limit theorem
2012/2/29
Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse imag...
Nice labeling problem for event structures: a counterexample
Nice labeling problem counterexample Combinatorics
2011/8/26
Abstract: In this note, we present a counterexample to a conjecture of Rozoy and Thiagarajan from 1991 (called also the nice labeling problem) asserting that any (coherent) event structure with finite...
An infinite-horizon optimal control problem and the stability of the adjoint variable (in Russian)
infinite-horizon optimal control problem stability adjoint variable
2011/2/21
Определения и обозначения. Пусть задано метрическое простран-ство X △= Rm. Определим T △= {t ∈ R| t ≥ 0}.
Realizability of Polytopes as a Low Rank Matrix Completion Problem
Realizability of Polytopes Low Rank Matrix Completion Problem
2011/2/22
Here we show that the problem of realizing a polytope with specified combinatorics is equivalent to a low rank matrix completion problem.This is comparable to known results reducing realizability to s...
The truncated matrix trigonometric moment problem: the operator approach
truncated matrix trigonometric moment problem operator approach
2011/1/19
The aim of this investigation is to obtain a bijective parameterization of all solutions of the truncated matrix trigonometric moment problem. Recall that the truncated matrix trigonometric moment pro...
The Kadison-Singer problem for the direct sum of matrix algebras
Kadison-Singer problem direct sum of matrix algebras
2010/12/3
Let Mn denote the algebra of complex n×n matrices and write M for the direct sum of the Mn. So a typical element of M has the form x = x1 ⊕ x2 · · · ⊕ xn ⊕ · · · ,where xn ∈ Mn and kxk = supn kxnk. We...
A mini-max problem for self-adjoint Toeplitz matrices
Toeplitz matrix Toeplitz operator trigonometric moment problems
2010/12/6
We study a minimum problem and associated maximum problem for finite, complex, self-adjoint Toeplitz matrices. If A is such a matrix, of size (N + 1)-by-(N + 1), we identify A with the operator it rep...