**A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode**
β_....the hyper-Catalan numbers πΆπ¦ count the number of subdivisions of a polygon into a given number of triangles, quadrilaterals, pentagons, etc. (its type π¦), and we show that their generating series solves a polynomial equation of a particular geometric form. This solution is straightforwardly extended to solve the general univariate polynomial equation._β
Wildberger, N. J. and Rubine, D. (2025) βA Hyper-Catalan Series Solution to Polynomial Equations, and the Geodeβ, The American Mathematical Monthly, pp. 1β20. doi: https://doi.org/10.1080/00029890.2025.2460966.
#OpenAccess #OA #Article #DOI #Maths #Mathematics #Math #Algebra #Polynomials #Academia #Academics
Bibliolater π π π
npub1h7β¦9r5fe
2025-05-01 19:32:37 GMT
Author Public Key
npub1h73dpngpam7elaxglnzskyzf0vsdxkcfj47t8yh8cmgr6my646cqv9r5feSeen on
wss://relay.mostr.pubPublished at
2025-05-01 19:32:37 GMTEvent JSON
{
"id": "db73f48495f3f96830daae53cf5a2d3781c1e4290ea1afbc1428d6713522e3c2",
"pubkey": "bfa2d0cd01eefd9ff4c8fcc50b10497b20d35b09957cb392e7c6d03d6c9aaeb0",
"created_at": 1746127957,
"kind": 1,
"tags": [
[
"t",
"openaccess"
],
[
"t",
"oa"
],
[
"t",
"article"
],
[
"t",
"doi"
],
[
"t",
"maths"
],
[
"t",
"mathematics"
],
[
"t",
"math"
],
[
"t",
"algebra"
],
[
"t",
"polynomials"
],
[
"t",
"academia"
],
[
"t",
"academics"
],
[
"proxy",
"https://qoto.org/users/bibliolater/statuses/114434241802085883",
"activitypub"
],
[
"client",
"Mostr",
"31990:6be38f8c63df7dbf84db7ec4a6e6fbbd8d19dca3b980efad18585c46f04b26f9:mostr",
"wss://relay.mostr.pub"
]
],
"content": "**A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode**\n\nβ_....the hyper-Catalan numbers πΆπ¦ count the number of subdivisions of a polygon into a given number of triangles, quadrilaterals, pentagons, etc. (its type π¦), and we show that their generating series solves a polynomial equation of a particular geometric form. This solution is straightforwardly extended to solve the general univariate polynomial equation._β\n\nWildberger, N. J. and Rubine, D. (2025) βA Hyper-Catalan Series Solution to Polynomial Equations, and the Geodeβ, The American Mathematical Monthly, pp. 1β20. doi: https://doi.org/10.1080/00029890.2025.2460966.\n\n#OpenAccess #OA #Article #DOI #Maths #Mathematics #Math #Algebra #Polynomials #Academia #Academics",
"sig": "9156b965681a751579f5a044c3de51cf9691d1ac9f26892adb0a6c79a3ec80c0dfab23a25fdca78f40d3650b0642777911ae7b48d1dd3ac25449a7a302a9de1e"
}