Pith Number

pith:75RFSSNE

pith:2011:75RFSSNEYXPZCBV4LBCFMLH6YH

not attested not anchored not stored refs pending

An explicit formula for the number of permutations with a given number of alternating runs

Shi-Mei Ma

arxiv:1110.6779 v2 · 2011-10-31 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{75RFSSNEYXPZCBV4LBCFMLH6YH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:08:03.304250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff625949a4c5df9106bc5844562cfec1e7fd40078b1f838efe8aadf7375cf679

Aliases

arxiv: 1110.6779 · arxiv_version: 1110.6779v2 · doi: 10.48550/arxiv.1110.6779 · pith_short_12: 75RFSSNEYXPZ · pith_short_16: 75RFSSNEYXPZCBV4 · pith_short_8: 75RFSSNE

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/75RFSSNEYXPZCBV4LBCFMLH6YH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ff625949a4c5df9106bc5844562cfec1e7fd40078b1f838efe8aadf7375cf679

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f98175e25be4f8699cf953127524eb80bbbfce936b67821e4aa378761e79c46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-31T12:58:39Z",
    "title_canon_sha256": "e883ef54c069d6fed8a95f7848bcc9f4f1eeb29f57cbc049762171ed1e653d98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6779",
    "kind": "arxiv",
    "version": 2
  }
}