We examine the Dual Ramsey Theorem and two related combinatorial principles VW(k, l) and OVW(k, l) from the perspectives of reverse mathematics and effective mathematics. We give a statement of the Dual Ramsey Theorem for open colorings in second order arithmetic and formalize work of Carlson and Simpson [1] to show that this statement implies ACA0 over RCA0. We show that neither VW(2, 2) nor O...

The generalized chain geometry over the local ring K(ε;σ) of twisted dual numbers, where K is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties as well as a geometric model in 4-space are investigated. Mathematics Subject Classification (2000): 51E05, 51B15, 51E20, 51E25, 51A45.

We show a way to compute, to a high level of precision, the probability that a randomly selected permutation of length n is non-overlapping. As a byproduct, we nd some combinatorial identities that are routine to prove using generating functions, but di cult to prove bijectively. Mathematics Subject Classi cation(2010). 05A16, 05A05, 05A10.

We give sufficient conditions for deriving moderately exponential and/or parameterized time approximation schemata (i.e., algorithms achieving ratios 1± , for arbitrarily small ) for broad classes of combinatorial optimization problems via a well-known technique widely used for deriving exact algorithms, namely the branching tree pruning. Mathematics Subject Classification. 68W25, 05C85, 68Q25....

We present a unified theory for permutation models of all the infinite families of finite and affine Weyl groups, including interpretations of the length function and the weak order. We also give new combinatorial proofs of Bott’s formula (in the refined version of Macdonald) for the Poincaré series of these affine Weyl groups. 1991 Mathematics Subject Classification. primary 20B35; secondary 0...

Assuming the continuum hypothesis there is an inseparable sequence of length ω1 that contains no Lusin subsequence, while if Martin’s Axiom and ¬CH is assumed then every inseparable sequence (of length ω1) is a union of countably many Lusin subsequences. 2000 Mathematics Subject Classification . 03E05 (Combinatorial set theory), 03E50 (Continuum hypothesis and Martin’s axiom), 03E35 ( Consisten...

We derive a combinatorial formula for quantized Donaldson-Thomas invariants of the m-loop quiver. Our main tools are the combinatorics of noncommutative Hilbert schemes and a degenerate version of the Cohomological Hall algebra of this quiver. 2010 Mathematics Subject Classification: Primary 16G20, secondary 05E05, 14N35

Words (strings of symbols) are fundamental in computer processing. Indeed, each bit of data processed by a computer is a string, and nearly all computer software use algorithms on strings. There are also abundant supply of applications of these algorithms in other areas such as data compression, DNA sequence analysis, computer graphics, cryptography, and so on. Combinatorics on words belongs to...

in recent years, mathematics is an essential aspect of all areas of daily life and the best predictor of being successful in economic situations of society. for many students, the mathematics accompanied with frustration, anxiety and negative attitudes towards mathematics. these students believe their anxiety have been derived from their math teachers, math misconception and weakness in math as...