5 problems

Let $V(n)$ be the Gessel-Viennot matrix associated with the graph $G(n)$, and let the paper's transit-free resolution identify the associated graph with the Aztec diamond graph. Th…

Conjecture 4. For all $k\geq 0$, the residue of $L_0(m)$ modulo $2^k$ is periodic with period dividing $2^k$; likewise, the residue of $L_1(m)$ modulo $2^k$ has period dividing…

Let $L(n)$, for $n\geq 0$, be the number of tilings of the Aztec diamond of order $n$ using horizontal skew tetrominos and square tetrominos. Write the multiplicity of 2 in the pri…

Let $M(n)$, for $n\geq 0$, be the number of tilings of the Aztec diamond of order $n$ using dominos and square tetrominos. Conjecture 2. For all $k\geq 1$, if … then … This is pres…

Let $M(n)$, for $n\geq 0$, be the number of tilings of the Aztec diamond of order $n$ using dominos and square tetrominos. Conjecture 1. For all $k\geq 1$, the residue of $M(n)$ mo…