5 problems

Let $p^0_i,q^0_i$ and $p^1_i,q^1_i$ enumerate, respectively, all losing positions of the forms $\{0,p^0_i,q^0_i\}$ and $\{1,p^1_i,q^1_i\}$, with each family arranged in increasing…

Let $p^0_i,q^0_i$ and $p^1_i,q^1_i$ denote the coordinates of the losing positions of the forms $\{0,p^0_i,q^0_i\}$ and $\{1,p^1_i,q^1_i\}$, respectively. Here, the pairs are compa…

Fix $(p,q)=(1,2)$ or $(p,q)=(2,3)$, and let $(a_n,b_n)$ be the associated sequences. Two sequences $(l_i)$ and $(u_i)$ are complementary when they are increasing and together parti…

Fix $p,q\in\mathbb{N}$, let $\pi=\pi_{p,q}$, and let $a=a(p,q)$ and $b=b(p,q)$ be the associated sequences. Let $U$ and $\mathbb{N}_0$ have the meanings fixed earlier in the paper,…

Fix $p,q\bin \mathbb{N}$, and let $a=a(p,q)$ and $b=b(p,q)$ denote the associated sequences. A pair $(p,q)$ is a splitting pair if it is a Wythoff pair or a dual Wythoff pair. The…