6 problems

Let $(X,\operatorname{\star})$ be a shelf, with distributive homology groups $H_n(X)$. A spindle is a shelf satisfying the additional spindle condition, and let…

Let $(X,\operatorname{\star})$ be a spindle, and let $\widetilde H^{N}_n(X)$ denote its normalized homology, with rank denoted by $\operatorname{rk}$. Normalized Rank Growth Conjec…

Let $(X,\operatorname{\star})$ be a shelf, with distributive homology groups $H_n(X)$ and rank denoted by $\operatorname{rk}$. Rank Growth Conjecture. For $n\geqslant |X|-2$, one h…

Let $L$ be a finite skew lattice, and let $L/\!\!\sim$ denote its quotient by the relevant equivalence relation. Assume that $L$ has either a unique minimum or a unique maximum. Ho…

Let $(X,\star)$ be a commutative spindle, meaning a set equipped with a self-distributive binary operation satisfying the spindle axioms. For $x,t\in X$, write…

Let $L$ be a semi-lattice with a projector, and let $H_n(L,t)$ denote its degree-$n$ distributive homology with coefficients determined by scalars $(a,b)$. Assume that…