{"arxiv_id":"1510.08192","incoming":{"papers":1,"sentences":1,"groups":[{"kind":"background","label":"Cites it as background","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1605.07727","title":"Lattice Complements and the Subadditivity of Syzygies of Simplicial Forests","url":"/paper/1605.07727","section":"Introduction","sentence":"These include some algebras of krull dimension at most 1 (Eisenbud, Huneke and Ulrich [ref] ), when $a=1$ (Fernández-Ramos and Gimenez [ref] if $I$ is generated by degree 2 monomials, Herzog and Srinivasan [ref] when $b$ is the projective dimension of $S/I$ or when $I$ is any monomial ideal), in certain homological degrees in the case of Gorenstein algebras (El Khoury and Srinivasan [ref] ) and the case $a=1,2,3$ for a monomial ideal generated in degree 2 (Abedelfatah and Nevo [ref] ).","intent_p":0.9,"contests_p":null}]}],"unlabelled_sentences":0},"outgoing":{"papers":3,"sentences":4,"groups":[{"kind":"background","label":"Cites as background","papers":3,"sentences":3,"quotes":[{"arxiv_id":"1303.6214","title":"A note on the subadditivity problem for maximal shifts in free resolutions","url":"/paper/1303.6214","section":"Introduction","sentence":"Given a graded ideal $I$ in $S$ let $t_i$ denote the maximal shifts in the minimal graded free $S$-resolution of $S/I$, namely [equation] The subadditivity relation [equation] was proved under certain conditions on $I$ or for certain values of $a$ and $b$, e.g. in [ref] , and is conjectured to hold under other conditions on $I$ for all values $a$ and $b$ [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"1602.02116","title":"A note on the subadditivity of Syzygies","url":"/paper/1602.02116","section":"Introduction","sentence":"Given a graded ideal $I$ in $S$ let $t_i$ denote the maximal shifts in the minimal graded free $S$-resolution of $S/I$, namely [equation] The subadditivity relation [equation] was proved under certain conditions on $I$ or for certain values of $a$ and $b$, e.g. in [ref] , and is conjectured to hold under other conditions on $I$ for all values $a$ and $b$ [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"1507.01183","title":"An alternative algorithm for computing the Betti table of a monomial ideal","url":"/paper/1507.01183","section":"Introduction","sentence":"For other recent results on other vanishing patterns, see e.g. [ref] .","intent_p":0.93,"contests_p":null}]}],"unlabelled_sentences":1},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1510.08192"}}