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Alternating sign matrices and totally symmetric plane partitions [Elektronski vir]Aigner, Florian ...Študiramo razvoj družine simetričnih polinomov (povezanih z izpopolnjenim preštevanjem matrik z alternirajočim predznakom glede na število inverzij, komplementarno število inverzij in položaj edine ... enice v zgornji vrstici) v Schurovih polinomih. Dokažemo, da lahko ta razvoj izrazimo kot vsoto po popolnoma simetričnih ravninskih razčlenitvah, in določimo koeficiente. To vzpostavlja novo povezavo med matrikami z alternirajočim predznakom in razredom ravninskih razčlenitev, kar dopolnjuje dejstvo, da je število matrik z alternirajočim predznakom enako številu popolnoma simetričnih sebi komplementarnih ravninskih razčlenitev ter tudi številu padajočih ravninskih razčlenitev. Kot stranski produkt dobimo zanimivo preslikavo iz popolnoma simetričnih ravninskih razčlenitev v Dyckove poti. Dokaz je osnovan na novi, dokaj splošni formuli za izražavo antisimetrizatorja z determinantami.Source: Proceedings of the 32nd International Conference on "Formal Power Series and Algebraic Combinatorics", July 6 - 24, 2020 (Online) [Elektronski vir] (12 str.)Type of material - conference contribution ; adult, seriousPublish date - 2020Language - englishCOBISS.SI-ID - 25233155
Author
Aigner, Florian |
Fischer, Ilse |
Konvalinka, Matjaž |
Nadeau, Philippe |
Tewari, Vasu
Topics
matrike z alternirajočim predznakom |
popolnoma simetrične ravninske razčlenitve |
Schurovi polinomi |
Catalanova števila |
alternating sign matrices |
totally symmetric plane partitions |
Schur polynomials |
Catalan numbers
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Aigner, Florian | ![]() |
Fischer, Ilse | ![]() |
Konvalinka, Matjaž | 22401 |
Nadeau, Philippe | ![]() |
Tewari, Vasu | ![]() |
Source: Personal bibliographies
and: SICRIS
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