scholarly journals A Simple Proof for the Number of Tilings of Quartered Aztec Diamonds

10.37236/3429 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Tri Lai
Keyword(s):  
Simple Proof ◽  
Aztec Diamond ◽  
Unpublished Work ◽  
Simple Product ◽  
Product Formulas

We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing its center. W. Jockusch and J. Propp (in an unpublished work) found that the number of tilings of quartered Aztec diamonds is given by simple product formulas. In this paper we present a simple proof for this result.

scholarly journals Lozenge Tiling Function Ratios for Hexagons with Dents on Two Sides

10.37236/9363 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Daniel Condon
Keyword(s):  
Triangular Lattice ◽  
Lozenge Tilings ◽  
Simple Product ◽  
Two Sides ◽  
Product Formulas

We give a formula for the number of lozenge tilings of a hexagon on the triangular lattice with unit triangles removed from arbitrary positions along two non-adjacent, non-opposite sides. Our formula implies that for certain families of such regions, the ratios of their numbers of tilings are given by simple product formulas.

scholarly journals A Simple Proof of the Aztec Diamond Theorem

10.37236/1915 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Sen-Peng Eu ◽  
Tung-Shan Fu
Keyword(s):  
Simple Proof ◽  
Lattice Paths ◽  
Hankel Determinants ◽  
Domino Tilings ◽  
Aztec Diamond ◽  
Schröder Numbers

Based on a bijection between domino tilings of an Aztec diamond and non-intersecting lattice paths, a simple proof of the Aztec diamond theorem is given by means of Hankel determinants of the large and small Schröder numbers.

scholarly journals A New Simple Proof of the Aztec Diamond Theorem

2015 ◽  
Vol 32 (4) ◽  
pp. 1389-1395 ◽  
Author(s):  
Manuel Fendler ◽  
Daniel Grieser
Keyword(s):  
Simple Proof ◽  
Aztec Diamond

The Strange Radicalism of Thomas Carnduff and St John Ervine

2017 ◽  
Author(s):  
Connal Parr
Keyword(s):  
Twentieth Century ◽  
Working Class ◽  
First World War ◽  
Class Consciousness ◽  
World War ◽  
Abbey Theatre ◽  
Unpublished Work ◽  
Early Twentieth Century ◽  
The First World War ◽  
First World

St John Ervine and Thomas Carnduff were born in working-class Protestant parts of Belfast in the 1880s, though Ervine would escape to an eventually prosperous existence in England. Orangeism, the politics of early twentieth-century Ireland, the militancy of the age—and the involvement of these writers in it—along with Ervine’s journey from ardent Fabian to reactionary Unionist, via his pivotal experiences managing the Abbey Theatre and losing a leg in the First World War, are all discussed. Carnduff’s own tumultuous life is reflected through his complicated Orange affiliation, gut class-consciousness, poetry, unpublished work, contempt for the local (and gentrified) Ulster artistic scene, and veneration of socially conscious United Irishman James Hope. It concludes with an assessment of their respective legacies and continuing import.

scholarly journals A simple proof of Andrews’s 5 F 4 evaluation

2013 ◽  
Vol 36 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ira M. Gessel
Keyword(s):  
Simple Proof

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

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