论文信息 - Tilings of quadriculated annuli

Tilings of quadriculated annuli

Tilings of a quadriculated annulus A are counted according to volume (in the formal variable q) and flux (in p). We consider algebraic properties of the resulting generating function ΦA(p, q). For q = -1, the non-zero roots in p must be roots of unity and for q > 0, real negative.

Nicolau C. Saldanha | Carlos Tomei

[1] W. J. Thron,et al. Encyclopedia of Mathematics and its Applications. , 1982 .

[2] F. R. Gantmakher. The Theory of Matrices , 1984 .

[3] Boris Hasselblatt,et al. Introduction to the Modern Theory of Dynamical Systems: LOCAL HYPERBOLIC THEORY AND ITS APPLICATIONS , 1995 .

[4] P. W. Kasteleyn. Dimer Statistics and Phase Transitions , 1963 .

[5] W. Thurston. Conway's tiling groups , 1990 .

[6] Peter Lancaster,et al. The theory of matrices , 1969 .

[7] Carlos Tomei,et al. On the determinant of the adjacency matrix for a planar sublattice , 1983, J. Comb. Theory, Ser. B.

[8] H. Halberstam,et al. Combinatorial Analysis , 1971, Nature.

[9] P. W. Kasteleyn. The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice , 1961 .

[10] J. Zukas. Introduction to the Modern Theory of Dynamical Systems , 1998 .

[11] Nicolau C. Saldanha,et al. Spaces of domino tilings , 1995, Discret. Comput. Geom..

[12] Michael Loss,et al. Fluxes, Laplacians and Kasteleyn's Theorem , 1992 .

[13] Greg Kuperberg,et al. Alternating-Sign Matrices and Domino Tilings (Part I) , 1992 .

[14] J. Propp,et al. Alternating sign matrices and domino tilings , 1991, math/9201305.

[15] R. MacKay. INTRODUCTION TO THE MODERN THEORY OF DYNAMICAL SYSTEMS (Encyclopaedia of Mathematics and its Applications 54) , 1997 .