{"paper":{"title":"Principal Specialization of Monomial Symmetric Polynomials and Group Determinants of Cyclic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Genki Shibukawa, Naoya Yamaguchi, Yuka Yamaguchi","submitted_at":"2022-03-28T00:16:20Z","abstract_excerpt":"In this paper, we study the principal specialization of monomial symmetric polynomials and investigate the special values of these polynomials at \\[ \\zeta_{(n,k)} := ( 1, \\zeta_n, \\zeta_n^2, \\dots, \\zeta_n^{kn-1} ), \\] where $\\zeta_n$ is a primitive $n$th root of unity. We give explicit formulas for several classes of special values. We also show that these special values naturally appear as the coefficients in the expansion of the $k$th power of the circulant determinant of order $n$ (the group determinant of the cyclic group of order $n$). These results extend Ore's formulas for the case $k "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.14422","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.14422/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}