Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Fabrizio Zanello"'
Autor:
William J. Keith, Fabrizio Zanello
We continue our study of the density of the odd values of eta-quotients, here focusing on the $m$-regular partition functions $b_m$ for $m$ even. Based on extensive computational evidence, we propose an elegant conjecture which, in particular, comple
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d3a8c6212f592df29e25f99b6f090bc2
Autor:
Fabrizio Zanello, James A. Sellers
Publikováno v:
International Journal of Number Theory. 17:1717-1728
Recently, Hirschhorn and the first author considered the parity of the function $a(n)$ which counts the number of integer partitions of $n$ wherein each part appears with odd multiplicity. They derived an effective characterization of the parity of $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec2f7e83e20c9b43e89ded057948139e
https://doi.org/10.1142/s1793042121500573
https://doi.org/10.1142/s1793042121500573
Autor:
Fabrizio Zanello
A famous conjecture of Parkin-Shanks predicts that $p(n)$ is odd with density $1/2$. Despite the remarkable amount of work of the last several decades, however, even showing this density is positive seems out of reach. In a 2018 paper with Judge, we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::999e96ccce3e12b1de8bb5c58d92516a
Publikováno v:
Differential Geometry and its Applications. 81:101866
We compare the integration by parts of contact forms - leading to the definition of the interior Euler operator - with the so-called canonical splittings of variational morphisms. In particular, we discuss the possibility of a generalization of the f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5f8e230b41bae186d11c89db16e40166
https://doi.org/10.1016/j.difgeo.2022.101866
https://doi.org/10.1016/j.difgeo.2022.101866
Autor:
Fabrizio Zanello, William J. Keith
We investigate the parity of the coefficients of certain eta-quotients, extensively examining the case of $m$-regular partitions. Our theorems concern the density of their odd values, in particular establishing lacunarity modulo 2 for specified coeff
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f0dcf0b6eaeb748ffd24ad990f3e6b6
http://arxiv.org/abs/2010.09881
http://arxiv.org/abs/2010.09881
Publikováno v:
Annals of Combinatorics. 22:583-600
The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2. Our main resul
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c754fe6830531faa51d3b18980e43b0c
https://doi.org/10.1007/s00026-018-0397-x
https://doi.org/10.1007/s00026-018-0397-x
Autor:
Fabrizio Zanello, Juan C. Migliore
Publikováno v:
Communications in Algebra. 46:2054-2062
The study of the h-vectors of graded Gorenstein algebras is an important topic in combinatorial commutative algebra, which despite the large amount of literature produced during the last several ye...
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https://explore.openaire.eu/search/publication?articleId=doi_________::9dfee8059bad113ba907fe9752587ce4
https://doi.org/10.1080/00927872.2017.1372457
https://doi.org/10.1080/00927872.2017.1372457
Autor:
Fabrizio Zanello, Juan C. Migliore
Publikováno v:
Proceedings of the American Mathematical Society. 145:1-9
We classify all possible $h$-vectors of graded artinian Gorenstein algebras in socle degree 4 and codimension $\leq 17$, and in socle degree 5 and codimension $\leq 25$. We obtain as a consequence that the least number of variables allowing the exist
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f0c961fb47b6317151e2b2aedb767c49
https://doi.org/10.1090/proc/13381
https://doi.org/10.1090/proc/13381
Autor:
Fabrizio Zanello
Publikováno v:
The Electronic Journal of Combinatorics. 25
F. Bergeron recently asked the intriguing question whether $\binom{b+c}{b}_q -\binom{a+d}{d}_q$ has nonnegative coefficients as a polynomial in $q$, whenever $a,b,c,d$ are positive integers, $a$ is the smallest, and $ad=bc$. We conjecture that, in fa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a16f426cbba2b8161df780f4989cd988
https://doi.org/10.37236/7358
https://doi.org/10.37236/7358
Roughly ten years ago, the following "Gorenstein Interval Conjecture" (GIC) was proposed: Whenever $(1,h_1,\dots,h_i,\dots,h_{e-i},\dots,h_{e-1},1)$ and $(1,h_1,\dots,h_i+\alpha,\dots,h_{e-i}+\alpha,\dots,h_{e-1},1)$ are both Gorenstein Hilbert funct
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ecc77415852321aa983bcdd34922e45