Sam Hopkins

### Questions (4)

 5 Decide if a given set of monomials is a basis of a polynomial ring quotient 3 Domain where for each ideal $I$ and each $a \in I$, $I = \langle a,b \rangle$ is Dedekind? 3 Induced isomorphism of homology implies isomorphism with coefficients in any group? 3 Why should the relative size of two sets depend on which other sets exist?

### Reputation (179)

 +20 Bijection between Dyck paths with $k$ peaks and $n+1-k$ peaks +30 When can the rank of a submodule be bigger than the rank of the module itself? +25 Decide if a given set of monomials is a basis of a polynomial ring quotient +5 Domain where for each ideal $I$ and each $a \in I$, $I = \langle a,b \rangle$ is Dedekind?

 3 When can the rank of a submodule be bigger than the rank of the module itself? 2 Bijection between Dyck paths with $k$ peaks and $n+1-k$ peaks

### Tags (12)

 3 modules 2 combinatorial-proofs 3 group-theory 0 commutative-algebra × 2 3 linear-algebra 0 groebner-basis 2 combinatorics × 2 0 set-theory 2 catalan-numbers 0 logic