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pro vyhledávání: '"05A18"'
Autor:
Defant, Colin, Lee, Mitchell
Defant found that the relationship between a sequence of (univariate) classical cumulants and the corresponding sequence of (univariate) free cumulants can be described combinatorially in terms of families of binary plane trees called troupes. Using
Externí odkaz:
http://arxiv.org/abs/2409.05219
Let $S_r(p,q)$ be the $r$-associated Stirling numbers of the second kind, the number of ways to partition a set of size $p$ into $q$ subsets of size at least $r$. For $r=1$, these are the standard Stirling numbers of the second kind, and for $r=2$, t
Externí odkaz:
http://arxiv.org/abs/2409.01489
Does $20$ have a friend? Or is it a solitary number? A folklore conjecture asserts that $20$ has no friends i.e. it is a solitary number. In this article, we prove that, a friend $N$ of $20$ is of the form $N=2\cdot5^{2a}m^2$ and it has atleast six d
Externí odkaz:
http://arxiv.org/abs/2409.04451
Autor:
Sagan, Bruce E, Swanson, Joshua
In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G. The Stirling
Externí odkaz:
http://arxiv.org/abs/2408.13874
Autor:
Liang, Jinting, Sagan, Bruce E.
We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal Lemma to prov
Externí odkaz:
http://arxiv.org/abs/2408.02782
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory has been developed primarily for specific applications in free probabi
Externí odkaz:
http://arxiv.org/abs/2407.17660
Autor:
Ehrenborg, Richard, Hetyei, Gábor
We study the poset of d-indivisible noncrossing partitions introduced by M\"uhle, Nadeau and Williams. These are noncrossing partitions such that each block has cardinality 1 modulo d and each block of the dual partition also has cardinality 1 modulo
Externí odkaz:
http://arxiv.org/abs/2407.08577
Autor:
Adell, José A.
We give explicit estimates for the Stirling numbers of the second kind $S(n,m)$. With a few exceptions, such estimates are asymptotically sharp. The form of these estimates varies according to $m$ lying in the central or non-central regions of $\{1,\
Externí odkaz:
http://arxiv.org/abs/2407.08246
Autor:
Bordianu, Andreea I., Cimpoeas, Mircea
Let $I$ be a squarefree monomial ideal of $S=K[x_1,\ldots,x_n]$. We prove that if $\operatorname{hdepth}(S/I)\leq 8$ or $n\leq 10$ then $\operatorname{hdepth}(I)\geq \operatorname{hdepth}(S/I)-1$.
Comment: 28 pages
Comment: 28 pages
Externí odkaz:
http://arxiv.org/abs/2407.04759
Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set $[n]=\{1,2,\dots,n\}$, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define the Fibonacc
Externí odkaz:
http://arxiv.org/abs/2407.04409