{"arxiv_id":"0908.3056","incoming":{"papers":3,"sentences":4,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1907.04668","title":"On the counting of $O(N)$ tensor invariants","url":"/paper/1907.04668","section":"The counting as a Kronecker sum","sentence":"To proceed with these sums, we will use a useful result by Howe [ref] (see also a result by Mizukawa, proposition 4.1 in [ref] , and also [ref] or a more recent use of it in [ref] ): ∑_γ∈S_n[S_2] χ^R(γ) = |S_n[S_2]| m^R where $m^R= 1$ if $R$ is an “even” partition, that is, all its row lengths are even, and $m^R=0$ otherwise.","intent_p":0.9,"contests_p":null},{"arxiv_id":"2005.01773","title":"On the counting tensor model observables as $U(N)$ and $O(N)$ classical invariants","url":"/paper/2005.01773","section":"Algebras and representation theoretic bases","sentence":"To tackle these sums, we use a result by Howe [ref] (see also [ref] ): $∑_γ∈S_n[S_2] χ^R(γ) = |S_n[S_2]| m^R$, where $m^R= 1$ if $R$ is an “even” partition, and $m^R=0$ otherwise.","intent_p":0.92,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1301.1560","title":"A basis for large operators in N=4 SYM with orthogonal gauge group","url":"/paper/1301.1560","section":"$SO(N)$ gauge theory","sentence":"In fact, from existing group theory results we know that the irrep $[A]$ of $S_n[S_2]$ is always subduced once [ref] .","intent_p":0.97,"contests_p":null}]}],"unlabelled_sentences":1},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"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/0908.3056"}}