Zobrazeno 1 - 10
of 980
pro vyhledávání: '"05A18"'
Autor:
Sabatini, Luca
Let $G$ be a permutation group on the finite set $\Omega$. We prove various results about partitions of $\Omega$ whose stabilizers have good properties. In particular, we obtain the following three theorems: In every solvable permutation group, there
Externí odkaz:
http://arxiv.org/abs/2411.18534
Autor:
Bordianu, Andreea I., Cimpoeas, Mircea
We study the Stanley depth and the Hilbert depth of the edge ideals of path graphs, cycle graphs, generalized star graphs and double broom graphs.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2411.10844
Autor:
Tarannikov, Yuriy
We prove that the number of partitions of the hypercube ${\bf Z}_q^n$ into $q^m$ subcubes of dimension $n-m$ each for fixed $q$, $m$ and growing $n$ is asymptotically equal to $n^{(q^m-1)/(q-1)}$. For the proof, we introduce the operation of the bang
Externí odkaz:
http://arxiv.org/abs/2411.04479
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