Elementary Chain Counting Problems

2000 ◽  
pp. 25-34
Keyword(s):  
Counting Problems ◽  
Elementary Chain

scholarly journals A computational proof of complexity of some restricted counting problems

2011 ◽  
Vol 412 (23) ◽  
pp. 2468-2485 ◽  
Author(s):  
Jin-Yi Cai ◽  
Pinyan Lu ◽  
Mingji Xia
Keyword(s):  
Counting Problems

scholarly journals Elementary chain composition of guinea pig thyroglobulin.

1975 ◽  
Vol 250 (18) ◽  
pp. 7294-7299 ◽  
Author(s):  
A Haeberli ◽  
J Bilstad ◽  
H Edelhoch ◽  
J E Rall
Keyword(s):  
Guinea Pig ◽  
Elementary Chain ◽  
Chain Composition

Media Clips: Boulder Lottery; The Probability of Slot Machines

2013 ◽  
Vol 107 (3) ◽  
pp. 172-175
Author(s):  
Kristy B. McGowan ◽  
Nathan J. Lowe Spicer
Keyword(s):  
Slot Machines ◽  
Counting Problems ◽  
State Lottery ◽  
The Media

Students analyze items from the media to answer mathematical questions related to the article. The clips this month, from the Colorado State lottery and a Marilyn vos Savant column on probability, involve probability and counting problems.

Informing Practice: Counting Using Sets of Outcomes

2012 ◽  
Vol 18 (3) ◽  
pp. 132-135 ◽  
Author(s):  
Elise Lockwood
Keyword(s):  
Counting Problems

A branch of mathematics—combinatorics—is explored through counting problems.

scholarly journals LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

1999 ◽  
Vol 14 (29) ◽  
pp. 4549-4574 ◽  
Author(s):  
C. R. GATTRINGER ◽  
S. JAIMUNGAL ◽  
G. W. SEMENOFF
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Algebraic Representation ◽  
Simple Derivation ◽  
Counting Problems ◽  
Intrinsic Geometry ◽  
Geometry Factor ◽  
Loop Expansion ◽  
Loop Surface

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

scholarly journals COUNTABLE MODELS OF THE THEORIES OF BALDWIN–SHI HYPERGRAPHS AND THEIR REGULAR TYPES

2019 ◽  
Vol 84 (3) ◽  
pp. 1007-1019
Author(s):  
DANUL K. GUNATILLEKA
Keyword(s):  
Large Body ◽  
Countable Model ◽  
Stable Theory ◽  
Generic Structure ◽  
Elementary Chain ◽  
Regular Type ◽  
Image Position ◽  
Original Class ◽  
Countable Models

AbstractWe continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11].

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