6 problems

Let $D_n$ and $S_n$ denote the Delannoy and Schröder numbers, respectively, defined by … Let $p>3$ be a prime. Sun's supercongruence. … This congruence was raised by Z.-W. Sun in 2…

Let $\operatorname{Av}(2413,3142)$ be the class of permutations avoiding $2413$ and $3142$, and let $S_n$ denote the large Schröder number of semilength $n$. Shapiro–Getu conjectur…

Let $p>3$ be a prime, and let $D_k$ and $S_k$ denote the central Delannoy and large Schröder numbers, respectively. Let $E_j$ denote the Euler numbers. Sun's conjecture. Sun conjec…

Let $S_{n,d}(q,t)$ be the $q,t$-Schröder number and let $\tilde{S}_{n,d}(q,t)$ be the little $q,t$-Schröder number. For odd $n$, let $X$ be the set of dissections of a regular…

Let $\delta_n$ denote the staircase shape, let $p(\delta_{n+2k}/\delta_n)$ be the number of pleasant diagrams of the skew shape $\delta_{n+2k}/\delta_n$, and let $s_n$ be the Schrö…

Let $p$ be a prime satisfying $p\equiv 2\pmod 3$. Let $T_k(3,3)$ and $M_k(3,3)$ denote the specialized sequences used in the paper. The author's conjecture. One has … This strength…