… " congruence mod 4, ie, those elements which differ from the height section used for the
construction of ,,~ by a multiple of 4… 4.3 we show the height sections for the four tilings in Fig. 4.2. …

… domino tiling of a figure will be called merely a tiling. Each tiling of a figure F consists of s(F)
dominoes… side of the congruence. Now, if we sum up over the set of all cycles, we obtain …

… We also prove a theorem about n-by-2n rectangles, that the number of domino tilings of the
n-by-2n rectangle is congruent to 1 modulo 4. Many other strange behaviors conjectured by …

… Instead of using domino-tilings, we will use an equivalent … However, if m is congruent to
2 (mod 4), then Дm 1Еm 2 is odd, … 1 when m is congruent to 2 (mod 4) and n is odd, and З1 …

… -adic behavior of the number of domino tilings of a 2n × 2n … (mod 4). Kasteleyn [K], and
Temperley and Fisher [TF], proved that the number of tilings of a 2n×2n square with 1 × 2 dominos …

… general phenomenon involving domino tilings of rectangles. … However, if m is congruent to
2 (mod 4), then (m−1)m/2 is odd… to be −1 when m is congruent to 2 (mod 4) and n is odd, and …

… a new set of tiles which we call the generalized dominoes of order k. We … congruent mod 4
to (0,2) or (2,0). A segment of length 1 is called a cut if there is no valid tiling of Γ in which a tile …

… tiling of infinitely many cells using only squares and dominoes is breakable at cell n, that is,
a square or a domino … our random tiling to be 1/0 and the probability of choosing a domino to …

… invariant Pt(q) that characterizes tilings that are “almost in the … domino tilings of such a region
is connected by flips and trits, a local move performed by removing three adjacent dominoes…

… combinatorially that the residue, modulo 4, of the number of domino tilings of a region with …
of domino tilings of a k × 2k rectangle is 1 mod 4. This is not the first time that domino tilings for …