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Paper Citation Record · LEDGER

Bijective recurrences concerning two Schr\"oder triangles

As of 16 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:1908.03912.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.03912 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:06:06.341652Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

24 of 24 outbound references displayed

  • verified exact0
  • verified fuzzy19
  • unresolved5
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 39f66c90-ab3a-453e-acc9-158b736b2d9f · outbound

This paper cites Barcucci, E.

Bijective recurrences concerning two Schr\"oder triangles Barcucci, E

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.752408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.203285Z digest=sha256:8f7c6db0a4fa833d0ed0fcb771e3a85c7c9406d402a2110bbd7446a4b089d656

Observation 0feb40ca-a8ca-466e-a1b2-e0540b6c79a5 · outbound

This paper cites Barry, Riordan Arrays: A Primer , Logic Press, Naas, Ireland (2016).

Bijective recurrences concerning two Schr\"oder triangles Barry, Riordan Arrays: A Primer , Logic Press, Naas, Ireland (2016)

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.739156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.209962Z digest=sha256:23064c56b5afcecb35592e6091075cd257c4b1e177b058b5290d34480f388391

Observation 8859b709-74eb-4081-b726-c4658dd92de9 · outbound

This paper cites an unresolved cited work.

Bijective recurrences concerning two Schr\"oder triangles Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:06:06.726137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.215075Z digest=sha256:bd9d5a814909a77c065fef884a744f386623b01775ab94a9f99d13ed06452e12

Observation 3cb1c83e-ba13-4eb5-a616-605d6fd963a7 · outbound

This paper cites Chen and Y.

Bijective recurrences concerning two Schr\"oder triangles Chen and Y

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.713431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.221994Z digest=sha256:b2f540b3eead61bfe1b642106a7854669b47fe14d1e2baf925bd40d0d97a6091

Observation a0d048d2-8f5a-4ce2-877d-b26bd1e9ff85 · outbound

This paper cites Claesson and S.

Bijective recurrences concerning two Schr\"oder triangles Claesson and S

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.697851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.228720Z digest=sha256:c1f70aef246b6066a432f513ac5691f020d6d1c6a104913d6e52286d35c5dd81

Observation f5bba065-37bb-4711-8fea-86ebc129ff38 · outbound

This paper cites Deutsch, L.

Bijective recurrences concerning two Schr\"oder triangles Deutsch, L

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.673931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.238858Z digest=sha256:21d2c30d33e24f7e3de20f17fa955ff19f3af7ef029bf5d96cd34aa54ef3e27d

Observation 1aae1b1d-fa97-4090-a648-864cbb25b160 · outbound

This paper cites an unresolved cited work.

Bijective recurrences concerning two Schr\"oder triangles Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:06:06.657595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.245777Z digest=sha256:2139471954fee1027e5a07780cdd88617c9815e512584a054d67395a793839ec

Observation 4ea99d6b-e79c-43ee-a087-136f8dd12319 · outbound

This paper cites an unresolved cited work.

Bijective recurrences concerning two Schr\"oder triangles Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:06:06.643932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.254248Z digest=sha256:6515fd9f65fedc3cbd488b70f6fb856a2f2da378f902a64a8839510d6d62ac8a

Observation 15882535-cfa2-4786-9e41-d8be5b54d219 · outbound

This paper cites Foata and D.

Bijective recurrences concerning two Schr\"oder triangles Foata and D

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.626102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.258956Z digest=sha256:0689c2a538098bca7f69e433e479191a7820c52a0b19ee05ba01182eaf56af73

Observation 5c75b5e8-053b-42b5-bdc3-970538a6eb6f · outbound

This paper cites He and R.

Bijective recurrences concerning two Schr\"oder triangles He and R

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.610409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.264433Z digest=sha256:1091beeb318c1ce03ca98aabf1b54497b9260f810d435a8c94235b395fd4b541

Observation 0762cc3c-1802-4c71-bde0-2010d31646c9 · outbound

This paper cites Kitaev, Patterns in permutations and words , Springer Science & Business Media (2011).

Bijective recurrences concerning two Schr\"oder triangles Kitaev, Patterns in permutations and words , Springer Science & Business Media (2011)

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.594895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.270632Z digest=sha256:f36904123e449fc8bd797f86184c639f9eb8edd572e04e5b4d380f1db97408c6

Observation f22eee20-e093-43a8-b14b-1c06b782ce90 · outbound

This paper cites Luzón, D.

Bijective recurrences concerning two Schr\"oder triangles Luzón, D

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.572902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.277839Z digest=sha256:b7912c9dd96b780c2e3884599d9ec85034c875975005412f543173480b9b8425

Observation e5fee72e-5b49-42b8-8f4e-ea359f05bc73 · outbound

This paper cites Merlini, D.G.

Bijective recurrences concerning two Schr\"oder triangles Merlini, D.G

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.554931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.282127Z digest=sha256:31d8c9a548706336c78fdf884fc5a006c31c8b648dd30d7b266c56c94c66f4c2

Observation 33f0dfc0-7ac0-46ad-8d2f-ca1d81cbb384 · outbound

This paper cites an unresolved cited work.

Bijective recurrences concerning two Schr\"oder triangles Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:06:06.536873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.286400Z digest=sha256:7c69900c1394d261aea859863f2b631f795b07efb2a440d24d0e0ca4d336c512

Observation 502265ce-0479-4817-8dc0-48bec69b5d14 · outbound

This paper cites Pergola and R.

Bijective recurrences concerning two Schr\"oder triangles Pergola and R

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.522057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.292967Z digest=sha256:b3f0a974337804bfe1dc1d768315492ff49589c9e6b7601200e778105c7ad97b

Observation 12402327-f17f-4d81-ab66-cf82456baa93 · outbound

This paper cites Rogers, Pascal triangles, Catalan numbers and renewal arrays , Discrete Math., 22 (1978): 301–310.

Bijective recurrences concerning two Schr\"oder triangles Rogers, Pascal triangles, Catalan numbers and renewal arrays , Discrete Math., 22 (1978): 301–310

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.508209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.302557Z digest=sha256:c5c8d699f07ffb930bf804896a6a29b983218c599f5fc902d1f02798a242d589

Observation 3a824de1-1785-4e88-9d62-fa8c20c981aa · outbound

This paper cites Shapiro, Bijections and the Riordan group , Theoret.

Bijective recurrences concerning two Schr\"oder triangles Shapiro, Bijections and the Riordan group , Theoret

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.494479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.308808Z digest=sha256:351883b14745cae652750650b007df45a5247fbbbd6b3f398347b5c3a7d19e2f

Observation f2d1f3e7-83de-4a97-b6f6-0896a35e3231 · outbound

This paper cites Shapiro, S.

Bijective recurrences concerning two Schr\"oder triangles Shapiro, S

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.479317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.314661Z digest=sha256:5f91f1d7b71adb9b17f9da6dfc9acfcf47f139b9081aa3bc40cbf787823335c7

Observation 2aa39955-a235-4960-9d4b-1a9a1b0aa34e · outbound

This paper cites Shapiro and A.B.

Bijective recurrences concerning two Schr\"oder triangles Shapiro and A.B

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.465042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.319230Z digest=sha256:e142df402adeb06f13b0846de3701d2d7dcde7ab96c05a48b2014051af4c97a1

Observation 24872526-c791-4e96-911c-8781c60b54c9 · outbound

This paper cites Sprugnoli, Riordan arrays and combinatorial sums , Discrete Math.

Bijective recurrences concerning two Schr\"oder triangles Sprugnoli, Riordan arrays and combinatorial sums , Discrete Math

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.448009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.323129Z digest=sha256:f0cce2a4975a9d420fcd58970286a81be257c7a5701d5f8948fcf8763552d37c

Observation e0233af2-8de6-487e-a866-f4a6e17dc4d3 · outbound

This paper cites Stanley, Enumerative Combinatorics, vol.

Bijective recurrences concerning two Schr\"oder triangles Stanley, Enumerative Combinatorics, vol

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.434501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.328696Z digest=sha256:50780114192e712486550408f3ae89ae5b0e91833a7c7c885db8618cfd61eb8e

Observation 4a4c22bc-63a9-4088-85a5-82bcc2f606fc · outbound

This paper cites an unresolved cited work.

Bijective recurrences concerning two Schr\"oder triangles Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:06:06.419270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.333219Z digest=sha256:66325d2c34efb8231b3d7f3d3d78db6c521e5bb950ab74848e5e6b6f11ee8b18

Observation f4b51513-5fb2-4c57-a8da-78a82c8e4cf7 · outbound

This paper cites West, Generating trees and the Catalan and Schröder numbers , Discrete Math.

Bijective recurrences concerning two Schr\"oder triangles West, Generating trees and the Catalan and Schröder numbers , Discrete Math

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.403376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.337217Z digest=sha256:f58ab48f6f793921c945506629306a424e45e3a9ab2ffcd8dd31886f3995ecb9

Observation 1d6965aa-0d9b-4339-ae42-a737ffd4bd9e · outbound

This paper cites Zhu, Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices , Proc.

Bijective recurrences concerning two Schr\"oder triangles Zhu, Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices , Proc

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:06:06.384082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:06:06.341652Z digest=sha256:e4ad9db96b8e142757991f9c890108897864418d136dd81f480e9d67c9092aeb

Pith citing papers

No inbound Pith citation observations are available.