Zobrazeno 1 - 10
of 2 723
pro vyhledávání: '"06A07"'
For each $n\geq 2$, we show that the class of all finite $n$-dimensional partial orders, when expanded with $n$ linear orders which realize the partial order, forms a Fra\"iss\'e class and identify its Fra\"iss\'e limit $(D_n,<,<_1,\ldots,<_n)$. We g
Externí odkaz:
http://arxiv.org/abs/2412.18704
Autor:
Anderson, Portia X., Banaian, Esther, Ferreri, Melanie J., Goff, Owen C., Hadaway, Kimberly P., Harris, Pamela E., Harry, Kimberly J., Mayers, Nicholas, Wang, Shiyun, Wilson, Alexander N.
For integral weights $\lambda$ and $\mu$ of a classical simple Lie algebra $\mathfrak{g}$, Kostant's weight multiplicity formula gives the multiplicity of the weight $\mu$ in the irreducible representation with highest weight $\lambda$, which we deno
Externí odkaz:
http://arxiv.org/abs/2412.16820
Autor:
Elizalde, Sergi, Lafrenière, Nadia, Lewis, Joel Brewster, McNicholas, Erin, Striker, Jessica, Welch, Amanda
We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional equation for the generating function of interval-closed sets of trunca
Externí odkaz:
http://arxiv.org/abs/2412.16368
Autor:
Yeats, Karen
The causal set theory d'Alembertian has rational coefficients for which alternating expressions are known. Here, a combinatorial interpretation of these numbers is given.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2412.14036
We introduce the notion of the free product of $q$-matroids, which is the $q$-analogue of the free product of matroids. We study the properties of this noncommutative binary operation, making an extensive use of the theory of cyclic flats. We show th
Externí odkaz:
http://arxiv.org/abs/2412.13025
Autor:
Malko, Artem
Following the classical results of Stong, we introduce a cohomological analogue of a core of a finite sheaved topological space and propose an algorithm for simplification in this category. In particular we generalize the notion of beat vertices and
Externí odkaz:
http://arxiv.org/abs/2412.11354
Let $\mathrm{Int}(n)$ denote the set of nonempty left weak Bruhat intervals in the symmetric group $\mathfrak{S}_n$. We investigate the equivalence relation $\overset{D}{\simeq}$ on $\mathrm{Int}(n)$, where $I \overset{D}{\simeq} J$ if and only if th
Externí odkaz:
http://arxiv.org/abs/2412.08413
Autor:
Campo, Frank A
The characterization of the finite minimal automorphic posets of width three is still an open problem. Niederle has shown that this task can be reduced to the characterization of the nice sections of width three having a non-trivial tower of nice sec
Externí odkaz:
http://arxiv.org/abs/2412.08363
The order polytopes arising from the finite poset were first introduced and studied by Stanley. For any positive integer $d\geq 14$, Liu and Tsuchiya proved that there exists a non-Ehrhart positive order polytope of dimension $d$. They also proved th
Externí odkaz:
http://arxiv.org/abs/2412.07164
Autor:
Aware, B. P., Bhavale, A. N.
In 2020 Bhavale and Waphare introduced the concept of a nullity of a poset as nullity of its cover graph. According to Bhavale and Waphare, if a dismantlable lattice of nullity k contains r reducible elements then 2 $\leq$ r $\leq$ 2k. In 2003 Pawar
Externí odkaz:
http://arxiv.org/abs/2412.03627