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For two vectors $a$ and $b$ in $V^*_n$ we have $a \\leq b$ if and only if $b - a$ belongs to the ground set of $V^*_n$.\n  We show that every interval in $V^*_n$ is shellable for $n$ at least 4. In order to obtain the result, we develop a new method for showing that a poset is shellable. This method differs from classical lexicographic shellability.\n  Shellability of interval"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.3159","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-14T14:02:46Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"f44bdeb491951d5b2b87d9b56e477c73b6f186e993f8e0c37aa4b624f8f095a9","abstract_canon_sha256":"a814a5d8270c335a8a2657eb3299888cb50fb9bb6882db4d03bb35517088e374"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:21.929386Z","signature_b64":"QWQIALsKOQZHmRvU+aWPZCHMzIoZiuhFdjhI+C/Qv6C1gk7KERCKk1HyJ9pQyk4V2XPqlvLA6CtnWrPuskMcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2441ddbff8e65d3c7f7c497b90f5af2e5bd816b76b8197dcb0da89a556d3e655","last_reissued_at":"2026-05-18T02:58:21.928917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:21.928917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shellability of the higher pinched Veronese posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Martin Tancer","submitted_at":"2013-05-14T14:02:46Z","abstract_excerpt":"The pinched Veronese poset $V^*_n$ is the poset with ground set consisting of all non-negative integer vectors of length n such that the sum of their coordinates is divisible by $n$ with exception of the vector $(1,...,1)$. For two vectors $a$ and $b$ in $V^*_n$ we have $a \\leq b$ if and only if $b - a$ belongs to the ground set of $V^*_n$.\n  We show that every interval in $V^*_n$ is shellable for $n$ at least 4. In order to obtain the result, we develop a new method for showing that a poset is shellable. 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