{"id":40997,"date":"2024-09-25T10:29:12","date_gmt":"2024-09-25T10:29:12","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%db%8c%da%a9-%d9%85%d8%b4%da%a9%d9%84-%d8%aa%d9%88%d8%b1%d8%a7%d9%86-%d8%af%d9%88%d8%a8%d8%ae%d8%b4%db%8c\/"},"modified":"2024-09-25T10:29:14","modified_gmt":"2024-09-25T10:29:14","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%db%8c%da%a9-%d9%85%d8%b4%da%a9%d9%84-%d8%aa%d9%88%d8%b1%d8%a7%d9%86-%d8%af%d9%88%d8%a8%d8%ae%d8%b4%db%8c","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%db%8c%da%a9-%d9%85%d8%b4%da%a9%d9%84-%d8%aa%d9%88%d8%b1%d8%a7%d9%86-%d8%af%d9%88%d8%a8%d8%ae%d8%b4%db%8c\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u06cc\u06a9 \u0645\u0634\u06a9\u0644 \u062a\u0648\u0631\u0627\u0646 \u062f\u0648\u0628\u062e\u0634\u06cc \u0647\u0627\u06cc\u067e\u0631\u06af\u0631\u0627\u0641 \u0628\u0627 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u06cc \u0639\u062c\u06cc\u0628 \u0648 \u063a\u0631\u06cc\u0628"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nA hypergraph bipartite Tur\u00e1n problem with odd uniformity<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u06cc\u06a9 \u0645\u0634\u06a9\u0644 \u062a\u0648\u0631\u0627\u0646 \u062f\u0648\u0628\u062e\u0634\u06cc \u0647\u0627\u06cc\u067e\u0631\u06af\u0631\u0627\u0641 \u0628\u0627 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u06cc \u0639\u062c\u06cc\u0628 \u0648 \u063a\u0631\u06cc\u0628<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nJie Ma, Tianchi Yang<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n13<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nCombinatorics,\u062a\u0631\u06a9\u06cc\u0628\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 7 March, 2024; originally announced March 2024.<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 7 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f.<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
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\n Semantic Scholar<\/a>
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\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

In this paper, we investigate the hypergraph Tur\u00e1n number $ex(n,K^{(r)}_{s,t})$. Here, $K^{(r)}_{s,t}$ denotes the $r$-uniform hypergraph with vertex set $\\left(\\cup_{i\\in [t]}X_i\\right)\\cup Y$ and edge set $\\{X_i\\cup \\{y\\}: i\\in [t], y\\in Y\\}$, where $X_1,X_2,\\cdots,X_t$ are $t$ pairwise disjoint sets of size $r-1$ and $Y$ is a set of size $s$ disjoint from each $X_i$. This study was initially explored by Erd\u0151s and has since received substantial attention in research. Recent advancements by Brada\u010d, Gishboliner, Janzer and Sudakov have greatly contributed to a better understanding of this problem. They proved that $ex(n,K_{s,t}^{(r)})=O_{s,t}(n^{r-\\frac{1}{s-1}})$ holds for any $r\\geq 3$ and $s,t\\geq 2$. They also provided constructions illustrating the tightness of this bound if $r\\geq 4$ is {\\it even} and $t\\gg s\\geq 2$. Furthermore, they proved that $ex(n,K_{s,t}^{(3)})=O_{s,t}(n^{3-\\frac{1}{s-1}-\\varepsilon_s})$ holds for $s\\geq 3$ and some $\u03b5_s>0$. Addressing this intriguing discrepancy between the behavior of this number for $r=3$ and the even cases, Brada\u010d et al. post a question of whether \\begin{equation*} \\mbox{$ex(n,K_{s,t}^{(r)})= O_{r,s,t}(n^{r-\\frac{1}{s-1}- \\varepsilon})$ holds for odd $r\\geq 5$ and any $s\\geq 3$.} \\end{equation*} In this paper, we provide an affirmative answer to this question, utilizing novel techniques to identify regular and dense substructures. This result highlights a rare instance in hypergraph Tur\u00e1n problems where the solution depends on the parity of the uniformity.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u060c \u0645\u0627 \u0628\u0647 \u0634\u0645\u0627\u0631\u0647 Hypergraph Tur\u00e1n $ ex (n \u060c k^{(r)} _ {s \u060c t}) $ \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u060c $ k^{(r)} _ {s \u060c t} $ $ hypergraph $ r $ -uniform \u0631\u0627 \u0628\u0627 vertex set $ \\ \u0633\u0645\u062a \u0686\u067e (\\ cup_ {i \\ in [t]} x_i \\ \u0631\u0627\u0633\u062a) \\ cup y $ $ \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f.\u0648 Edge $ \\ {x_i \\ cup \\ {y \\}: i \\ in [t] \u060c y \\ in y \\} $ \u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 $ x_1 \u060c x_2 \u060c \\ cdots \u060c x_t $ $ t $ \u0645\u062c\u0645\u0648\u0639\u0647 \u0647\u0627\u06cc \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0627\u0632 \u0627\u0646\u062f\u0627\u0632\u0647 \u0627\u0633\u062a$ R-1 $ \u0648 $ y $ \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u0627\u0646\u062f\u0627\u0632\u0647 $ S $ \u062c\u062f\u0627 \u0627\u0632 \u0647\u0631 $ x_i $ \u0627\u0633\u062a.\u0627\u06cc\u0646 \u0645\u0637\u0627\u0644\u0639\u0647 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u062a\u0648\u0633\u0637 ERD\u0151S \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a \u0648 \u0627\u0632 \u0622\u0646 \u0632\u0645\u0627\u0646 \u062a\u0648\u062c\u0647 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u062f\u0631 \u062a\u062d\u0642\u06cc\u0642\u0627\u062a \u062f\u0627\u0634\u062a\u0647 \u0627\u0633\u062a.\u067e\u06cc\u0634\u0631\u0641\u062a \u0647\u0627\u06cc \u0627\u062e\u06cc\u0631 \u062a\u0648\u0633\u0637 Brada\u010d \u060c Gishboliner \u060c Janzer \u0648 Sudakov \u062a\u0627 \u062d\u062f \u0632\u06cc\u0627\u062f\u06cc \u062f\u0631 \u062f\u0631\u06a9 \u0628\u0647\u062a\u0631 \u0627\u06cc\u0646 \u0645\u0634\u06a9\u0644 \u0646\u0642\u0634 \u062f\u0627\u0634\u062a\u0647 \u0627\u0633\u062a.\u0622\u0646\u0647\u0627 \u062b\u0627\u0628\u062a \u06a9\u0631\u062f\u0646\u062f \u06a9\u0647 $ ex (n \u060c k_ {s \u060c t}^{(r)}) = o_ {s \u060c t} (n^{r- \\ frac {1} {s-1}}) $ \u0628\u0631\u0627\u06cc \u0647\u0631$ r \\ geq 3 $ \u0648 $ s \u060c t \\ geq 2 $.\u0622\u0646\u0647\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0633\u0627\u062e\u062a\u0627\u0631\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0627\u062f\u0646\u062f \u06a9\u0647 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0633\u0641\u062a\u06cc \u0627\u06cc\u0646 \u0645\u062d\u062f\u0648\u062f\u0647 \u0627\u0633\u062a \u0627\u06af\u0631 $ r \\ geq 4 $ {\\ It} \u0648 $ t \\ gg s \\ geq 2 $ \u0628\u0627\u0634\u062f.\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646 \u060c \u0622\u0646\u0647\u0627 \u062b\u0627\u0628\u062a \u06a9\u0631\u062f\u0646\u062f \u06a9\u0647 $ ex (n \u060c k_ {s \u060c t}^{(3)}) = o_ {s \u060c t} (n^{3- \\ frac {1} {s-1}-\\ varepsilon_s}) $ \u0628\u0631\u0627\u06cc $ s \\ geq 3 $ \u0648 \u0628\u0631\u062e\u06cc $ \u03b5_s> 0 $ \u0646\u06af\u0647 \u0645\u06cc \u062f\u0627\u0631\u062f.\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0627\u062e\u062a\u0644\u0627\u0641 \u062c\u0630\u0627\u0628 \u0628\u06cc\u0646 \u0631\u0641\u062a\u0627\u0631 \u0627\u06cc\u0646 \u0634\u0645\u0627\u0631\u0647 \u0628\u0631\u0627\u06cc $ r = 3 $ \u0648 \u0645\u0648\u0627\u0631\u062f \u062d\u062a\u06cc \u060c Brade\u010d \u0648 \u0647\u0645\u06a9\u0627\u0631\u0627\u0646.\u06cc\u06a9 \u0633\u0624\u0627\u0644 \u0631\u0627 \u0627\u0631\u0633\u0627\u0644 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0622\u06cc\u0627 \\ start {\u0645\u0639\u0627\u062f\u0644\u0647*} \\ mbox {$ ex (n \u060c k_ {s \u060c t}^{(r)}) = o_ {r \u060c s \u060c t} (n^{r- \\ frac {1} {s-1}- \\ varepsilon}) $ \u0628\u0631\u0627\u06cc \u0639\u062c\u06cc\u0628 \u0648 \u063a\u0631\u06cc\u0628 $ r \\ geq 5 $ \u0648 \u0647\u0631 $ s \\ geq 3 $ \u0646\u06af\u0647 \u0645\u06cc \u062f\u0627\u0631\u062f.\u060c \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u06a9\u0646\u06cc\u06a9 \u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u0632\u06cc\u0631 \u0633\u0627\u062e\u062a \u0647\u0627\u06cc \u0645\u0646\u0638\u0645 \u0648 \u0645\u062a\u0631\u0627\u06a9\u0645.\u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u06cc\u06a9 \u0646\u0645\u0648\u0646\u0647 \u0646\u0627\u062f\u0631 \u062f\u0631 \u0645\u0634\u06a9\u0644\u0627\u062a Hypergraph Tur\u00e1n \u0631\u0627 \u0628\u0631\u062c\u0633\u062a\u0647 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0645\u062d\u0644\u0648\u0644 \u0628\u0647 \u0628\u0631\u0627\u0628\u0631\u06cc \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u06cc \u0628\u0633\u062a\u06af\u06cc \u062f\u0627\u0631\u062f.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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