corpus.blog
41554 blogs · [ { "id": "01a087e9-ec66-7269-aeac-12d0598aff3a", "title": "Multivariate polynomial representations of the infinite dihedral group", "url": "https://tcjpn.wordpress.com/2026/08/04/multivariate-polynomial-representations-of-the-infinite-dihedral-group/", "published_at": "2026-08-05T04:07:49+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d059ec5e8b", "title": "Refinement of Kreweras’ relation between the faces of the associahedra and restricted noncrossing partitions of the root system A_n", "url": "https://tcjpn.wordpress.com/2026/06/11/refinement-of-kreweras-relation-between-the-faces-of-the-associahedra-and-restricted-noncrossing-partitions-of-the-root-system-a_n/", "published_at": "2026-06-11T15:33:35+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05a690288", "title": "Hypercubes and reciprocals of power series", "url": "https://tcjpn.wordpress.com/2026/03/24/hypercubes-and-reciprocals-of-power-series/", "published_at": "2026-03-25T01:56:11+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05ab3b7ca", "title": "Section 2: Compilations for m=3 to m=-3 of “As Above, So Below: (m)-associahedra and (m)-noncrossing partitions polynomials”", "url": "https://tcjpn.wordpress.com/2026/03/01/section-2-compilations-for-m3-to-m-3-of-as-above-so-below-m-associahedra-and-m-noncrossing-partitions-polynomials/", "published_at": "2026-03-01T23:01:22+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05b83583a", "title": "Resonance", "url": "https://tcjpn.wordpress.com/2025/02/20/resonance/", "published_at": "2025-02-20T15:40:30+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05be9395f", "title": "Boil and bubble: Conjuring the digamma and log(D) by umbrally mixing the logarithm with the Bernoulli function", "url": "https://tcjpn.wordpress.com/2024/12/31/boil-and-bubble-conjuring-the-digamma-and-logd-by-umbrally-mixing-the-logarithm-with-the-bernoulli-function/", "published_at": "2025-01-01T06:25:47+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05c2c9721", "title": "Bernoulli number umbral translation / polynomial umbral substitution operator and binomial Sheffer polynomial sequences", "url": "https://tcjpn.wordpress.com/2024/12/19/bernoulli-number-umbral-translation-polynomial-umbral-substitution-operator-and-binomial-sheffer-polynomial-sequences/", "published_at": "2024-12-19T08:38:51+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05c8bf910", "title": "The Joy of Polygammary: Umbral witchcraft and the polygamma functions vis a vis the Bernoulli function", "url": "https://tcjpn.wordpress.com/2024/12/11/the-joy-of-polygammary-umbral-witchcraft-and-the-polygamma-functions-vis-a-vis-the-bernoulli-function/", "published_at": "2024-12-12T00:52:24+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05cfe3e75", "title": "On Euler’s derivation of the e.g.f. of the Bernoulli numbers", "url": "https://tcjpn.wordpress.com/2024/10/08/on-eulers-derivation-of-the-e-g-f-of-the-bernoulli-numbers/", "published_at": "2024-10-08T19:22:50+00:00" }, { "id": "01a087e9-ec66-7269-aeac-12d05d49f426", "title": "The Thermodynamic 3-D Permutahedron", "url": "https://tcjpn.wordpress.com/2024/08/26/the-thermodynamic-3-d-permutahedron/", "published_at": "2024-08-26T17:31:49+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb16840c9266", "title": "Umbral witchcraft with Bernoulli and Blissard", "url": "https://tcjpn.wordpress.com/2024/08/25/umbral-witchcraft-with-bernoulli-and-blissard/", "published_at": "2024-08-25T21:06:49+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb16844529a8", "title": "The Scottish Cafe", "url": "https://tcjpn.wordpress.com/2024/03/05/the-scottish-cafe/", "published_at": "2024-03-06T05:12:27+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb168449e2c3", "title": "A Schur Thing – Appendix to As Above, So Below: The Up-Down Operators for the (m)-Associahedra Partition Polynomials", "url": "https://tcjpn.wordpress.com/2023/08/24/a-schur-thing-appendix-to-as-above-so-below-the-up-down-operators-for-the-m-associahedra-partition-polynomials/", "published_at": "2023-08-25T03:56:01+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb1684eadd1c", "title": "(m)-Associahedra and (m)-Noncrossing Partition Polynomials and the Infinite Dihedral Group", "url": "https://tcjpn.wordpress.com/2023/07/26/m-associahedra-and-m-noncrossing-partition-polynomials-and-the-infinite-dihedral-group/", "published_at": "2023-07-26T18:31:53+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb16857a52da", "title": "Iterative formula for the Kreweras-Voiculescu polynomials–the noncrossing partitions polynomials", "url": "https://tcjpn.wordpress.com/2023/07/19/iterative-formula-for-the-kreweras-voiculescu-polynomials-the-noncrossing-partitions-polynomials/", "published_at": "2023-07-20T00:56:56+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb1685949e3f", "title": "Noncrossing partitions and (-1)-associahedra partition polynomials as Appell and quasi-Appell sequences", "url": "https://tcjpn.wordpress.com/2023/07/09/noncrossing-partitions-and-1-associahedra-partition-polynomials-as-appell-and-quasi-appell-sequences/", "published_at": "2023-07-10T03:54:24+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb1685fc41f1", "title": "The umbral compositional inverse of a Sheffer polynomial sequence and its lowering and raising operators", "url": "https://tcjpn.wordpress.com/2023/07/04/the-umbral-compositional-inverse-of-a-sheffer-polynomial-sequence-and-its-lowering-and-raising-operators/", "published_at": "2023-07-05T05:54:33+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb1686f39c0d", "title": "Reps of the lowering / destruction / annihilation operator for binomial Sheffer polynomial sequences", "url": "https://tcjpn.wordpress.com/2023/06/30/reps-of-the-lowering-destruction-annihilation-operator-for-binomial-sheffer-polynomial-sequences/", "published_at": "2023-07-01T04:30:18+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb16871f5714", "title": "A Catalan Identity Related to Fibonacci Polynomials and Its Generalization to the Fuss-Catalan Number Sequences", "url": "https://tcjpn.wordpress.com/2023/05/31/a-catalan-identity-related-to-fibonacci-polynomials-and-its-generalization-to-the-fuss-catalan-number-sequences/", "published_at": "2023-06-01T06:08:25+00:00" }, { "id": "01a0dd72-8a20-7122-a520-bb16877f33e8", "title": "Lagrange à la Laguerre: Compositional inverse of a reduction of the (m)-noncrossing partitions / refined (m)-Narayana partition polynomials", "url": "https://tcjpn.wordpress.com/2023/05/31/lagrange-a-la-laguerre-compositional-inverse-of-a-reduction-of-the-m-noncrossing-partitions-refined-m-narayana-partition-polynomials/", "published_at": "2023-05-31T16:27:20+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a4497909", "title": "As Above, So Below: (m)-associahedra and (m)-noncrossing partitions polynomials", "url": "https://tcjpn.wordpress.com/2023/05/11/as-above-so-below-m-associahedra-and-m-noncrossing-partitions-polynomials/", "published_at": "2023-05-12T01:58:52+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a4f474e0", "title": "(m)-Associahedra and (-m)-Noncrossing Partition Polynomials as Moments of Umbral Inverse Appell Polynomial Sequences", "url": "https://tcjpn.wordpress.com/2023/04/28/m-associahedra-and-m-noncrossing-partition-polynomials-as-moments-of-umbral-inverse-appell-polynomial-sequences/", "published_at": "2023-04-28T20:37:01+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a54250fd", "title": "Interpretations of the (−m)−Fuss-Narayana numbers for m>0", "url": "https://tcjpn.wordpress.com/2023/04/23/interpretations-of-the-%e2%88%92m%e2%88%92fuss-narayana-numbers-for-m0/", "published_at": "2023-04-23T22:58:24+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a584fa30", "title": "Inverse Log Associahedra Polynomials, a.k.a. Inverse Generalized Zernike Polynomials", "url": "https://tcjpn.wordpress.com/2023/04/03/inverse-log-associahedra-polynomials-a-k-a-inverse-generalized-zernike-polynomials/", "published_at": "2023-04-04T05:19:06+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a635e759", "title": "Log Narayana polynomials and the raising ops for the noncrossing and special Schur partition polynomials", "url": "https://tcjpn.wordpress.com/2023/04/02/log-narayana-polynomials-and-the-raising-ops-for-the-noncrossing-and-special-schur-partition-polynomials/", "published_at": "2023-04-02T18:57:09+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a72b7433", "title": "Generalized Zernike polynomials and the raising ops for the associahedra and the inverse noncrossing partition polynomials", "url": "https://tcjpn.wordpress.com/2023/04/01/generalized-zernike-polynomials-and-the-raising-ops-for-the-associahedra-and-the-inverse-noncrossing-partition-polynomials/", "published_at": "2023-04-02T06:12:42+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a7f0aa5a", "title": "Resume for the (m)-associahedra and (m)-noncrossing partitions polynomials", "url": "https://tcjpn.wordpress.com/2023/03/23/resume-for-the-m-associahedra-and-m-noncrossing-partitions-polynomials/", "published_at": "2023-03-24T00:29:28+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a861a458", "title": "Laurent series and o.g.f.s and e.g.f.s, oh my! Narayana and Catalan versus Euler and Grassmann", "url": "https://tcjpn.wordpress.com/2023/03/19/laurent-series-and-o-g-f-s-and-e-g-f-s-oh-my-narayana-and-catalan-versus-euler-and-grassmann/", "published_at": "2023-03-19T18:28:24+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a890c5cd", "title": "Combinatorics for a generalized Lagrange inversion formula and the (±m)-associahedra and (±m)-noncrossing partitions", "url": "https://tcjpn.wordpress.com/2023/03/16/combinatorics-for-a-generalized-lagrange-inversion-formula-and-the-%c2%b1m-associahedra-and-%c2%b1m-noncrossing-partitions/", "published_at": "2023-03-16T17:38:10+00:00" }, { "id": "01a0dd87-33a0-700e-a5b7-3a59a8c1ac6d", "title": "As Above, So Below: Dualities, combinatorial reciprocities, and the associahedra and noncrossing partitions of the Weyl-Coxeter group A_n", "url": "https://tcjpn.wordpress.com/2023/03/12/as-above-so-below-dualities-combinatorial-reciprocities-and-the-associahedra-and-noncrossing-partitions-of-the-weyl-coxeter-group-latex-a_n/", "published_at": "2023-03-13T04:46:13+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc4169181e", "title": "A Doubly Infinite Ladder: The m-associahedra, the m- noncrossing partitions, raising and lowering operations, and combinatorial reciprocity for m an integer", "url": "https://tcjpn.wordpress.com/2023/03/08/combinatorial-reciprocity-the-m-associahedra-and-the-m-noncrossing-partitions-for-m-an-integer/", "published_at": "2023-03-08T16:23:17+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc41ad2cf0", "title": "Compilation of OEIS Partition Polynomials A133314, A134685, A145271, A356144, and A356145", "url": "https://tcjpn.wordpress.com/2022/10/08/compilation-of-oeis-partition-polynomials-a133314-a134685-a145271-a356144-and-a356145/", "published_at": "2022-10-08T23:46:29+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc426a1d89", "title": "The Bernoulli function: Integration, summation, and the Hurwitz and Riemann zeta functions", "url": "https://tcjpn.wordpress.com/2022/09/28/the-bernoulli-function-integration-summation-and-the-hurwitz-and-riemann-zeta-functions/", "published_at": "2022-09-28T21:06:41+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc429ed9ec", "title": "The Norlund Self-Convolutional Bernoulli Polynomials and Derivatives as Finite Differences", "url": "https://tcjpn.wordpress.com/2022/09/27/the-norlund-self-convolutional-bernoulli-polynomials-part-i-in-differential-calculus/", "published_at": "2022-09-28T00:48:08+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc4326189c", "title": "The reduced inverse refined Eulerian polynomials and associated arrays", "url": "https://tcjpn.wordpress.com/2022/08/18/the-reduced-inverse-refined-eulerian-polynomials-and-associated-arrays/", "published_at": "2022-08-18T22:17:35+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc440977a2", "title": "The Gang of Five: A series inversion group", "url": "https://tcjpn.wordpress.com/2022/08/03/the-gang-of-five-an-inversion-group/", "published_at": "2022-08-03T17:58:53+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc4419d3d4", "title": "Schur expansion coefficients, generalized Faber polynomials, convolutions, and umbral identities", "url": "https://tcjpn.wordpress.com/2022/08/02/schur-expansion-coefficients-generalized-faber-polynomials-convolutions-and-umbral-identities/", "published_at": "2022-08-02T17:42:31+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc4451a774", "title": "Generalized Schur Expansion Koefficients", "url": "https://tcjpn.wordpress.com/2022/08/02/generalized-schur-expansion-koefficients/", "published_at": "2022-08-02T17:19:35+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc44ab161f", "title": "One Matrix to Rule Them All", "url": "https://tcjpn.wordpress.com/2022/07/27/one-matrix-to-rule-them-all/", "published_at": "2022-07-27T07:30:32+00:00" }, { "id": "01a0dd95-b874-7232-98e0-17cc452a4472", "title": "Matryoshka Dolls: Iterated noncrossing partitions, the refined Narayana group, and quantum fields", "url": "https://tcjpn.wordpress.com/2022/07/08/iterated-noncrossing-partitions-and-quantum-fields/", "published_at": "2022-07-09T01:02:05+00:00" } ] posts Claim your blog
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2026

Multivariate polynomial representations of the infinite dihedral grouporiginal ↗
5 Aug 2026
Refinement of Kreweras’ relation between the faces of the associahedra and restricted noncrossing partitions of the root system A_noriginal ↗
11 Jun 2026
Hypercubes and reciprocals of power seriesoriginal ↗
25 Mar 2026
Section 2: Compilations for m=3 to m=-3 of “As Above, So Below: (m)-associahedra and (m)-noncrossing partitions polynomials”original ↗
1 Mar 2026

2025

Resonanceoriginal ↗
20 Feb 2025
Boil and bubble: Conjuring the digamma and log(D) by umbrally mixing the logarithm with the Bernoulli functionoriginal ↗
1 Jan 2025

2024

Bernoulli number umbral translation / polynomial umbral substitution operator and binomial Sheffer polynomial sequencesoriginal ↗
19 Dec 2024
The Joy of Polygammary: Umbral witchcraft and the polygamma functions vis a vis the Bernoulli functionoriginal ↗
12 Dec 2024
On Euler’s derivation of the e.g.f. of the Bernoulli numbersoriginal ↗
8 Oct 2024
The Thermodynamic 3-D Permutahedronoriginal ↗
26 Aug 2024
Umbral witchcraft with Bernoulli and Blissardoriginal ↗
25 Aug 2024
The Scottish Cafeoriginal ↗
6 Mar 2024

2023

A Schur Thing – Appendix to As Above, So Below: The Up-Down Operators for the (m)-Associahedra Partition Polynomialsoriginal ↗
25 Aug 2023
(m)-Associahedra and (m)-Noncrossing Partition Polynomials and the Infinite Dihedral Grouporiginal ↗
26 Jul 2023
Iterative formula for the Kreweras-Voiculescu polynomials–the noncrossing partitions polynomialsoriginal ↗
20 Jul 2023
Noncrossing partitions and (-1)-associahedra partition polynomials as Appell and quasi-Appell sequencesoriginal ↗
10 Jul 2023
The umbral compositional inverse of a Sheffer polynomial sequence and its lowering and raising operatorsoriginal ↗
5 Jul 2023
Reps of the lowering / destruction / annihilation operator for binomial Sheffer polynomial sequencesoriginal ↗
1 Jul 2023
A Catalan Identity Related to Fibonacci Polynomials and Its Generalization to the Fuss-Catalan Number Sequencesoriginal ↗
1 Jun 2023
Lagrange à la Laguerre: Compositional inverse of a reduction of the (m)-noncrossing partitions / refined (m)-Narayana partition polynomialsoriginal ↗
31 May 2023
As Above, So Below: (m)-associahedra and (m)-noncrossing partitions polynomialsoriginal ↗
12 May 2023
(m)-Associahedra and (-m)-Noncrossing Partition Polynomials as Moments of Umbral Inverse Appell Polynomial Sequencesoriginal ↗
28 Apr 2023
Interpretations of the (−m)−Fuss-Narayana numbers for m>0original ↗
23 Apr 2023
Inverse Log Associahedra Polynomials, a.k.a. Inverse Generalized Zernike Polynomialsoriginal ↗
4 Apr 2023
Log Narayana polynomials and the raising ops for the noncrossing and special Schur partition polynomialsoriginal ↗
2 Apr 2023
Generalized Zernike polynomials and the raising ops for the associahedra and the inverse noncrossing partition polynomialsoriginal ↗
2 Apr 2023
Resume for the (m)-associahedra and (m)-noncrossing partitions polynomialsoriginal ↗
24 Mar 2023
Laurent series and o.g.f.s and e.g.f.s, oh my! Narayana and Catalan versus Euler and Grassmannoriginal ↗
19 Mar 2023
Combinatorics for a generalized Lagrange inversion formula and the (±m)-associahedra and (±m)-noncrossing partitionsoriginal ↗
16 Mar 2023
As Above, So Below: Dualities, combinatorial reciprocities, and the associahedra and noncrossing partitions of the Weyl-Coxeter group A_noriginal ↗
13 Mar 2023
A Doubly Infinite Ladder: The m-associahedra, the m- noncrossing partitions, raising and lowering operations, and combinatorial reciprocity for m an integeroriginal ↗
8 Mar 2023

2022

Compilation of OEIS Partition Polynomials A133314, A134685, A145271, A356144, and A356145original ↗
8 Oct 2022
The Bernoulli function: Integration, summation, and the Hurwitz and Riemann zeta functionsoriginal ↗
28 Sept 2022
The Norlund Self-Convolutional Bernoulli Polynomials and Derivatives as Finite Differencesoriginal ↗
28 Sept 2022
The reduced inverse refined Eulerian polynomials and associated arraysoriginal ↗
18 Aug 2022
The Gang of Five: A series inversion grouporiginal ↗
3 Aug 2022
Schur expansion coefficients, generalized Faber polynomials, convolutions, and umbral identitiesoriginal ↗
2 Aug 2022
Generalized Schur Expansion Koefficientsoriginal ↗
2 Aug 2022
One Matrix to Rule Them Alloriginal ↗
27 Jul 2022
Matryoshka Dolls: Iterated noncrossing partitions, the refined Narayana group, and quantum fieldsoriginal ↗
9 Jul 2022