Geodesic
A generalization of descent polynomials
Mathematics and Education in Mathematics, Tome 51 (2022), pp. 145-150.

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The notion of a descent polynomial, a function in enumerative combinatorics that counts permutations with specific properties, enjoys a revived recent research interest due to its connection with other important notions in combinatorics, viz. peak polynomials and symmetric functions. We define the function d m(I, n) as a generalization of the descent polynomial and obtain an explicit formula for d m(I, n) when m is sufficiently large. В комбинаториката спускащият се полином e функция, с която се изброяват пермутации със специфични свойства. В последните години интересът към него е подновен поради връзката му с други важни понятия в комбинаториката като върхови полиноми и симетрични функции. Дефинираме функцията d m(I, n) като обобщение на спускащия се полином и извеждаме явна формула за d m(I, n), когато m е достатъчно голямо.
Keywords: descent polynomial, permutation, generalization, multiplicity, repetitions, 05A05, спускащ се полином, пермутация, обобщение, многочисленост, повторения 
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     author = {Raychev, Angel},
     title = {A generalization of descent polynomials},
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     pages = {145--150},
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     volume = {51},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MEM_2022_51_a11/}
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Raychev, Angel. A generalization of descent polynomials. Mathematics and Education in Mathematics, Tome 51 (2022), pp. 145-150. http://geodesic.mathdoc.fr/item/MEM_2022_51_a11/