14 problems

Let $a=(a_0,\dots,a_n)$ be a sequence of non-negative integers, let $x^{(a)}$ be the alphabet defined by … and write $|a|=a_0+\cdots+a_n$. For a composition $v=(v_0,\dots,v_n)$, wr…

Let $p$ be the parameter of the $D_2$ identity, let $t$ be an indeterminate, and let $\operatorname{Res}_{x_0,x_1,x_2,x_3,x_4}$ denote the iterated residue in the displayed variabl…

Let $m>2$, let $p$ be the parameter of the $D_m$ identity, let $t$ be an indeterminate, and let $\operatorname{Res}_{x_0,x_1,\ldots,x_{m+2}}$ denote the iterated residue in the dis…

Let $m$ and $p$ be the parameters of the $A_m$ constant-term identity, let $t$ be an indeterminate, and let $\operatorname{Res}_{x_0,x_1,\ldots,x_{m+1}}$ denote the iterated residu…

Let $h_{p,m}(t)$ and $\tilde{h}_{p,m}(t)$ be the polynomials defined by the factorizations of the residue polynomials $H_{p,m}(t)$ and $\tilde{H}_{p,m}(t)$ for the $D_m$ orbifold v…

Let $n$ be a positive integer, let $a,b,k$ be arbitrary nonnegative integers, and let $m,n_0\leq n\leq m+n_0$. Theorem a-f asserts a specific constant-term product formula for…

Let $n$ be a positive integer, let $M\subset\{1,2,\dots,n\}$, and for each $s\in M$ choose an index $r_s$ such that $r_s\notin M$. Let $\boldsymbol{a}=(a_1,\dots,a_n)$ be nonnegati…

Let $n\equiv\zeta\pmod 4$ with $\zeta\in\{0,1\}$, let $u\in\mathbb C$ satisfy … and let $\tau_{ij}$ and $\sigma_{ij}$ be signatures satisfying the paper's condition. Write…

Adamović–Milas logarithmic constant term conjecture. For odd positive integer $n$ and nonnegative integer $k$, set $m=(n-1)/2$ and $K=2k+1$. Then

Constant-term conjecture. This constant term equals

Let $I=\{i_1,\ldots,i_m\}$ be a proper subset of $\{0,1,\ldots,n\}$ and let $J=\{j_1,\ldots,j_m\}$ be a multi-subset of $\{0,1,\ldots,n\}\setminus I$, where…

Let $D_p(n_1,\ldots,n_p;n_0;a,b,k;q)$ be the constant term … where $\widetilde J_\alpha$ is determined by the prescribed block sizes. Write $[r]_q!$ for the $q$-factorial and let…

Let $D_1(n_0;n_1;a,b;q)$ be the constant term of the Laurent polynomial … Here $\operatorname{CT}$ denotes the constant term, $(x;q)_k$ is the $q$-shifted factorial, and $\Gamma_q$…

Let $k$ and $m$ be positive integers. For variables $x_1,\ldots,x_{2k+1}$, let $\operatorname{CT}_{x_1,\ldots,x_{2k+1}}$ denote the constant term in their Laurent expansion. Then t…