@article{Ayyer2015ASM, AUTHOR = {Ayyer, Arvind}, TITLE = {A statistical model of current loops and magnetic monopoles}, JOURNAL = {Math. Phys. Anal. Geom.}, FJOURNAL = {Mathematical Physics, Analysis and Geometry. An International Journal Devoted to the Theory and Applications of Analysis and Geometry to Physics}, VOLUME = {18}, YEAR = {2015}, NUMBER = {1}, PAGES = {Art. 16, 19}, DOI = {10.1007/s11040-015-9185-6}, } @article{TRENCH1985199, title = {On the eigenvalue problem for Toeplitz band matrices}, journal = {Linear Algebra and its Applications}, volume = {64}, pages = {199-214}, year = {1985}, doi = {https://doi.org/10.1016/0024-3795(85)90277-0}, author = {William F. Trench}, abstract = {A formula is given for the characteristic polynomial of an nth order Toeplitz band matrix, with bandwidth k < n, in terms of the zeros of a kth degree polynomial with coefficients independent of n. The complexity of the formula depends on the bandwidth k, and not on the order n. Also given is a formula for eigenvectors, in terms of the same zeros and k coefficients which can be obtained by solving a k × k homogeneous system.} } @book {chapterXEulerian, AUTHOR = {Fleischner, Herbert}, TITLE = {Eulerian graphs and related topics. {P}art 1. {V}ol. 1}, SERIES = {Annals of Discrete Mathematics}, VOLUME = {45}, PUBLISHER = {North-Holland Publishing Co., Amsterdam}, YEAR = {1990}, PAGES = {xiv+387}, } @article{KASTELEYN19611209, title = {The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice}, journal = {Physica}, volume = {27}, number = {12}, pages = {1209-1225}, year = {1961}, doi = {https://doi.org/10.1016/0031-8914(61)90063-5}, author = {P.W. Kasteleyn}, abstract = {The number of ways in which a finite quadratic lattice (with edges or with periodic boundary conditions) can be fully covered with given numbers of “horizontal” and “vertical” dimers is rigorously calculated by a combinatorial method involving Pfaffians. For lattices infinite in one or two dimensions asymptotic expressions for this number of dimer configurations are derived, and as an application the entropy of a mixture of dimers of two different lengths on an infinite rectangular lattice is calculated. The relation of this combinatorial problem to the Ising problem is briefly discussed.} } @article{Kasteleyn1963, author = {Kasteleyn,P. W. }, title = {Dimer Statistics and Phase Transitions}, journal = {Journal of Mathematical Physics}, volume = {4}, number = {2}, pages = {287-293}, year = {1963}, doi = {10.1063/1.1703953}, } @article{Fisher, title = {Statistical Mechanics of Dimers on a Plane Lattice}, author = {Fisher, Michael E.}, journal = {Phys. Rev.}, volume = {124}, issue = {6}, pages = {1664--1672}, numpages = {0}, year = {1961}, publisher = {American Physical Society}, doi = {10.1103/PhysRev.124.1664} } @article{TemperleyFisher, author = { H. N. V. Temperley and Michael E. Fisher }, title = {Dimer problem in statistical mechanics-an exact result}, journal = {The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics}, volume = {6}, number = {68}, pages = {1061-1063}, year = {1961}, publisher = {Taylor & Francis}, doi = {10.1080/14786436108243366} } @book{BondyGT, AUTHOR = {Bondy, J. A. and Murty, U. S. R.}, TITLE = {Graph theory}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {244}, PUBLISHER = {Springer, New York}, YEAR = {2008}, PAGES = {xii+651}, DOI = {10.1007/978-1-84628-970-5}, } @unpublished{arora-ayyer-2022, author = {Anita Arora and Arvind Ayyer}, title = {The monopole-dimer model for cartesian products of graphs}, note={In preparation} } @article {hammersley-menon-1970, AUTHOR = {Hammersley, J. M. and Menon, V. V.}, TITLE = {A lower bound for the monomer-dimer problem}, JOURNAL = {J. Inst. Math. Appl.}, FJOURNAL = {Journal of the Institute of Mathematics and its Applications}, VOLUME = {6}, YEAR = {1970}, PAGES = {341--364}, DOI = {10.1093/imamat/6.4.341}, } @article{wu2006, Author = {F. Wu}, Date-Added = {2013-09-22 09:25:56 +0000}, Date-Modified = {2013-09-22 11:17:28 +0000}, Doi = {10.1103/PhysRevE.74.020104}, fJournal = {Physical Review E}, journal = {Phys. Rev. E (3)}, Number = {2}, Title = {Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary}, Volume = {74}, Year = {2006}, Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.74.020104}, } @article{jerrum1987, Author = {Jerrum, Mark}, fJournal = {Journal of Statistical Physics}, journal = {J. Stat. Phys.}, Number = {1}, Pages = {121--134}, Publisher = {Springer}, Title = {Two-dimensional monomer-dimer systems are computationally intractable}, Volume = {48}, Year = {1987}, DOI = {10.1007/BF01010403}, } @article{heilmann1972, Author = {Heilmann, Ole J. and Lieb, Elliott H.}, Journal = {Communications in Mathematical Physics}, Number = {3}, Pages = {190--232}, Publisher = {Springer}, Title = {Theory of monomer-dimer systems}, Volume = {25}, Year = {1972}, } @article {ayyer-2020, AUTHOR = {Ayyer, Arvind}, TITLE = {Squareness for the monopole-dimer model}, JOURNAL = {Ann. Combin.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {24}, YEAR = {2020}, NUMBER = {2}, PAGES = {237--255}, DOI = {10.1007/s00026-019-00480-5}, } @book{AandS-1964, title={Handbook of mathematical functions with formulas, graphs, and mathematical tables}, author={Abramowitz, Milton and Stegun, Irene A}, volume={55}, year={1964}, publisher={US Government printing office} } @book {TableOfIntegrals2000, AUTHOR = {Gradshteyn, I. S. and Ryzhik, I. M.}, TITLE = {Table of integrals, series, and products}, EDITION = {Sixth}, NOTE = {Translated from the Russian, Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger}, PUBLISHER = {Academic Press Inc., San Diego, CA}, YEAR = {2000}, PAGES = {xlvii+1163}, } @article{Cayley1849, author = {A. Cayley}, doi = {doi:10.1515/crll.1849.38.93}, url = {https://doi.org/10.1515/crll.1849.38.93}, title = {Sur les déterminants gauches. (Suite du Mémoire T. XXXII. p. 119).}, journal = {}, number = {38}, volume = {1849}, year = {1849}, pages = {93--96} }